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Paper's Title:
Applications of Relations and Relators in the
Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H-4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
Ulam Stability of Reciprocal Difference and Adjoint Functional Equations
Author(s):
K. Ravi, J. M. Rassias and B. V. Senthil Kumar
Department of Mathematics,
Sacred Heart College, Tirupattur - 635601,
India
Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE
Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam - 632 509, India
shckavi@yahoo.co.in
jrassias@primedu.uoa.gr
bvssree@yahoo.co.in
Abstract:
In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or Ulam-Gavruta-Rassias) stability problem for the same equations.
Paper's Title:
Hyers-Ulam-Rassias Stability
of a Generalized Jensen Functional Equation
Author(s):
A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani
Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr
bbouikhalene@yahoo.fr
Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com
Redouani-ahmed@yahoo.fr
Abstract:
In this paper we obtain the Hyers-Ulam-Rassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the Hyers-Ulam-stability of the K-spherical (n × n)-matrix functional equation.
Paper's Title:
Ulam Stability of Functional Equations
Author(s):
Stefan Czerwik and Krzysztof Król
Institute of Mathematics
Silesian University of Technology
Kaszubska 23,
44-100 Gliwice,
Poland
Stefan.Czerwik@polsl.pl
Krzysztof.Krol@polsl.pl
Abstract:
In this survey paper we present some of the main results on Ulam-Hyers-Rassias stability for important functional equations.
Paper's Title:
On Stan Ulam and his Mathematics
Author(s):
Krzysztof Ciesielski and Themistocles M. Rassias
Mathematics Institute, Jagiellonian University,
Abstract:
In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.
Paper's Title:
On the Generalized Stability and
Asymptotic Behavior of Quadratic Mappings
Author(s):
Hark-Mahn Kim, Sang-Baek Lee and Eunyoung Son
Department of Mathematics
Chungnam National University
Daejeon,
305-764,
Republic of Korea
hmkim@cnu.ac.kr
Abstract:
We extend the stability of quadratic mappings to the stability of general quadratic mappings with several variables, and then obtain an improved asymptotic property of quadratic mappings on restricted domains.
Paper's Title:
Stability of Almost Multiplicative Functionals
Author(s):
Norio Niwa, Hirokazu Oka, Takeshi Miura and Sin-Ei Takahasi
Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa 572-8530,
Japan
Faculty of Engineering, Ibaraki University,
Hitachi 316-8511,
Japan
Department of Applied Mathematics and Physics, Graduate School of
Science and Engineering,
Yamagata University,
Yonezawa 992-8510
Japan
oka@mx.ibaraki.ac.jp
miura@yz.yamagata-u.ac.jp
sin-ei@emperor.yz.yamagata-u.ac.jp
Abstract:
Let
δ
and p be non-negative real numbers. Let
be the
real or complex number field and
a normed algebra
over
. If a mapping
satisfies
then we show that
φ
is multiplicative or
for all
If, in
addition,
φ
satisfies
for some p≠1, then by using Hyers-Ulam-Rassias
stability of additive Cauchy equation, we show that
φ
is a ring homomorphism or
for all
In other words,
φ
is a ring homomorphism, or an approximately zero
mapping. The results of this paper are inspired by Th.M. Rassias' stability
theorem.
Paper's Title:
Fixed Points and Stability
of the Cauchy Functional Equation
Author(s):
Choonkil Park and Themistocles M. Rassias
Department of Mathematics, Hanyang University,
Seoul 133-791,
Republic of Korea
Department of Mathematics,
National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece
baak@hanyang.ac.kr
trassias@math.ntua.gr
Abstract:
Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the Cauchy functional equation.
Paper's Title:
Approximation of an AQCQ-Functional Equation and its Applications
Author(s):
Choonkil Park and Jung Rye Lee
Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133-791,
Korea;
Department of Mathematics,
Daejin University,
Kyeonggi 487-711,
Korea
baak@hanyang.ac.kr
jrlee@daejin.ac.kr
Abstract:
This paper is a survey on the generalized Hyers-Ulam stability of an AQCQ-functional equation in several spaces. Its content is divided into the following sections:
1. Introduction and preliminaries.
2. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: direct method.
3. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: fixed point method.
4. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: direct method.
5. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: fixed point method.
6. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: direct method.
7. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: fixed point method.
Paper's Title:
A Fixed Point Approach to
the Stability of the Equation
Author(s):
Soon-Mo Jung
Mathematics Section, College of Science and Technology
Hong-Ik
University, 339-701 Chochiwon
Republic of Korea.
smjung@hongik.ac.kr
Abstract:
We will apply a fixed point method for proving the Hyers--Ulam stability of
the functional equation
.
Paper's Title:
On the Ulam Stability for Euler-Lagrange Type Quadratic Functional Equations
Author(s):
Matina John Rassias and John Michael Rassias
Statistics and Modelling Science,
University of Strathclyde,
Livingstone Tower,
26 Richmond Str,
Glasgow, Uk, G1 1xh
Pedagogical Department, E. E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str, Aghia Paraskevi,
Athens 15342, Greece
Abstract:
In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem.
In 1941 D.H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin
has been the second author treating the Ulam problem for additive mappings. In 1978 according
to P.M. Gruber this kind of stability problems is of particular interest in probability theory and in
the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam
stability for the Ulam problem for different mappings. In 1992-2000 J.M. Rassias investigated
the Ulam stability for Euler-Lagrange mappings. In this article we solve the Ulam problem
for Euler-Lagrange type quadratic functional equations. These stability results can be applied
in mathematical statistics, stochastic analysis, algebra, geometry, as well as in psychology and
sociology.
Paper's Title:
Stability of a Mixed Additive, Quadratic and Cubic Functional Equation In Quasi-Banach Spaces
Author(s):
A. Najati and F. Moradlou
Department of Mathematics, Faculty of Sciences,
University of Mohaghegh Ardabili, Ardabil,
Iran
a.nejati@yahoo.com
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz,
Iran
moradlou@tabrizu.ac.ir
Abstract:
In this paper we establish the general solution of a mixed additive,
quadratic and cubic functional equation and investigate the
Hyers--Ulam--Rassias stability of this equation in quasi-Banach
spaces. The concept of Hyers-Ulam-Rassias stability originated from
Th. M. Rassias' stability theorem that appeared in his paper: On the
stability of the linear mapping in Banach spaces, Proc. Amer. Math.
Soc. 72 (1978), 297--300.
Paper's Title:
Asymptotic Behavior of Mixed Type Functional Equations
Author(s):
J. M. Rassias
Pedagogical Department, E.E., National and
Capodistrian University of Athens, Section of Mathematics And Informatics, 4, Agamemnonos
Str., Aghia Paraskevi, Athens 15342,Greece
jrassias@primedu.uoa.gr
URL:
http://www.primedu.uoa.gr/~jrassias/
Abstract:
In 1983 Skof [24] was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 Jung [14] investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by Jung [14], in 1998 and by the author [21], in 2002. Besides we establish new theorems about the Ulam stability of mixed type functional equations on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.
Paper's Title:
Solution of the Hyers-Ulam Stability Problem for Quadratic Type Functional Equations in Several Variables
Author(s):
John Michael Rassias
Pedagogical Department, E.E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str., Aghia Paraskevi,
Athens 15342,
Greece
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/
Abstract:
In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P. M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam stability for the Ulam problem for different mappings. In this article we solve the Hyers-Ulam problem for quadratic type functional equations in several variables. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.
Paper's Title:
Stability of a Pexiderized Equation
Author(s):
Maryam Amyar
Department of Mathematics,
Islamic Azad University, Rahnamaei Ave,
Mashhad 91735, Iran,
and Banach Mathematical Research Group (BMRG)
amyari@mshdiau.ac.ir
URL: http://amyari.mshdiau.ac.ir
Abstract:
The aim of the paper is to prove the
stability of the Pexiderized equation f(x)=g(y+x)-h(y-x), for any
amenable abelian group.
Paper's Title:
On a Method of Proving the Hyers-Ulam Stability
of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchor
Abstract:
We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable
Paper's Title:
Hyperbolic Barycentric Coordinates
Author(s):
Abraham A. Ungar
Department of Mathematics, North Dakota State University,
Fargo, ND 58105,
USA
Abraham.Ungar@ndsu.edu
URL: http://math.ndsu.nodak.edu/faculty/ungar/
Abstract:
A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.
Paper's Title:
The Superstability of the Pexider Type Trigonometric Functional Equation
Author(s):
Gwang Hui Kim and Young Whan Lee
Department of Mathematics, Kangnam
University Yongin, Gyeonggi, 446-702, Korea.
ghkim@kangnam.ac.kr
Department of Computer and Information Security
Daejeon University, Daejeon 300-716, Korea.
ywlee@dju.ac.kr
Abstract:
The aim of this paper is to investigate the stability
problem for
the Pexider type (hyperbolic) trigonometric functional equation
f(x+y)+f(x+σy)=λg(x)h(y) under the conditions :
|f(x+y)+f(x+σy)- λg(x)h(y)|≤φ(x),
φ(y), and min {φ(x), φ (y)}.
As a consequence, we have generalized the results of stability for
the cosine(d'Alembert), sine, and the Wilson functional equations by J.
Baker, P. Găvruta, R. Badora and R. Ger, Pl.~Kannappan, and G.
H. Kim
Paper's Title:
On Some
Mapping Properties of M
Author(s):
Nihal Yilmaz Özgür
Balkesir University,
Faculty of Arts and Sciences, Department of Mathematics,
10145 Balkesir,
TURKEY
nihal@balikesir.edu.tr
URL: http://w3.balikesir.edu.tr/~nihal/
Abstract:
We consider spheres corresponding to any norm function on the complex plane and their images under the Möbius transformations. We see that the sphere preserving property is not an invariant characteristic property of Möbius transformations except in the Euclidean case.
Paper's Title:
On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations
Author(s):
Javad Izadi and Bahmann Yousefi
Department of Mathematics, Payame Noor
University,
P.O. Box: 19395-3697, Tehran,
Iran.
E-mail: javadie2003@yahoo.com,
b_yousefi@pnu.ac.ir
Abstract:
Let A be a Lie Banach*-algebra. For each elements (a, b) and (c, d) in A2:= A * A, by definitions
(a, b) (c, d)= (ac, bd),
|(a, b)|= |a|+ |b|,
(a, b)*= (a*, b*),
A2 can be considered as a Banach*-algebra. This Banach*-algebra is called a Lie Banach*-algebra whenever it is equipped with the following definitions of Lie product:
for all a, b, c, d in A. Also, if A is a Lie Banach*-algebra, then D: A2→A2 satisfying
D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]
for all $a, b, c, d∈A, is a Lie derivation on A2. Furthermore, if A is a Lie Banach*-algebra, then D is called a Lie* derivation on A2 whenever D is a Lie derivation with D (a, b)*= D (a*, b*) for all a, b∈A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach*-algebra homomorphisms and Lie* derivations on the Banach*-algebra A2.
Paper's Title:
A Stability of the G-type Functional Equation
Author(s):
Gwang Hui Kim
Department of Mathematics, Kangnam University
Suwon 449-702, Korea.
ghkim@kangnam.ac.kr
Abstract:
We will investigate the stability in the sense of G
Paper's Title:
Power and Euler-Lagrange Norms
Author(s):
Mohammad Sal Moslehian and John Michael Rassias
Department of Mathematics,
Ferdowsi University,
P. O. Box 1159, Mashhad 91775,
Iran;
Department of Pure Mathematics,
University of Leeds,
Leeds LS2 9JT,
United Kingdom.
moslehian@ferdowsi.um.ac.ir
URL: http://www.um.ac.ir/~moslehian/
Pedagogical Department, E.E., Section of Mathematics and Informatics
National and Capodistrian University of Athens,
4, Agamemnonos str., Aghia Paraskevi, Attikis 15342, Athens,
Greece.
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/
Abstract:
We introduce the notions of power and Euler-Lagrange norms by
replacing the triangle inequality, in the definition of norm, by
appropriate inequalities. We prove that every usual norm is a power
norm and vice versa. We also show that every norm is an
Euler-Lagrange norm and that the converse is true under certain
condition.
Paper's Title:
Stability Problems for Generalized Additive Mappings and Euler-Lagrange Type Mappings
Author(s):
M. Todoroki, K. Kumahara, T. Miura and S.-E. Takahasi
The Open University of Japan,
Chiba, 261-8586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp
Yamagata University,
Yonezawa 992-8510,
Japan
miura@yz.yamagata-u.ac.jp
Toho University, Yamagata University,
Chiba, 273-0866,
Japan
sin_ei1@yahoo.co.jp
Abstract:
We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.
Paper's Title:
Superquadracity, Bohr's Inequality and Deviation from a Mean Value
Author(s):
S. Abramovich, J. Barić, and J. Pečarić
Department of Mathematics, University of Haifa,
Haifa, 31905,
Israel
FESB, University of Split,
Rudera Bošcovića,
B.B., 21000, Split,
Croatia
jbaric@fesb.hr
Faculty of Textile Technology,
University of Zagreb,
Prilaz Baruna Filipovića,
30, 10000 Zagreb,
Croatia.
pecaric@hazu.hr
Abstract:
Extensions of Bohr's inequality via superquadracity are obtained, where instead of the power p=2 which appears in Bohr's inequality we get similar results when we deal with p≥ 2 and with p≤ 2. Also, via superquadracity we extend a bound for deviation from a Mean Value.
Paper's Title:
Using Direct and Fixed Point Technique of Cubic Functional Equation and its Hyers-Ulam Stability
Author(s):
Ramanuja Rao Kotti, Rajnesh Krishnan Mudaliar, Kaushal Neelam Devi, Shailendra Vikash Narayan
Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
URL: https://www.fnu.ac.fj
Abstract:
In this present work, we introduce a new type of finite dimensional cubic functional equation of the form
where Φ≥4 is an integer, and derive its general solution. The main purpose of this work is to investigate the Hyers-Ulam stability results for the above mentioned functional equation in Fuzzy Banach spaces by means of direct and fixed point methods.
Paper's Title:
A Note on the Ulam stability of Reciprocal Difference and Adjoint Functional Equations
Author(s):
K. Ravi, J. M. Rassias, M. E. Gordji, and B. V. Senthil Kumar
Department of Mathematics,
Sacred Heart College, Tirupattur - 635601,
India
shckavi@yahoo.co.in
Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE
jrassias@primedu.uoa.gr
Department of Mathematics, Semnan
University,
P.O. Box 35195-363, Semnan,
Iran
madjid.eshaghi@gmail.com
Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam - 632 509,
India
bvssree@yahoo.co.in
Abstract:
This note is an erratum to previous work published as Volume 8, Issue 1, Paper 13, 2011 of The Australian Journal of Mathematical Analysis and Applications.
Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir1,2
1Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
The Functional Equation With an Exponential Polynomial Solution and its Stability
Author(s):
Young Whan Lee1, Gwang Hui Kim2*, and Jeong Il Kim3
1Department of Computer
Hacking and Information Security,
College of Engineering, Daejeon University,
Daejeon, 34520,
Korea(Republic of).
E-mail: ywlee@dju.ac.kr
2Department of Mathematics,
Kangnam University,
Yongin, Gyeonggi, 16979,
Korea(Republic of).
E-mail: ighkim@kangnam.ac.kr
3Department of Statistics,
Daejeon University,
Daejeon 34520,
Korea(Republic of).
E-mail: jlkim@dju.ac.kr
Abstract:
In this paper, we prove that the unique continuous solution of the functional equation
is
where pn(x) is a polynomial with degree n and
We also obtain the superstability and stability of the functional equation with the following forms, respectively:
and
Paper's Title:
Norm Estimates for the Difference between Bochner’s Integral and the Convex Combination of Function’s Values
Author(s):
P. Cerone, Y.J. Cho, S.S. Dragomir, J.K. Kim, and S.S. Kim
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
pietro.cerone@vu.edu.au
URL:
http://rgmia.vu.edu.au/cerone/index.html
Department of
Mathematics Education, College of Education,
Gyeongsang National University, Chinju 660-701, Korea
yjcho@nongae.gsnu.ac.kr
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Department of
Mathematics, Kyungnam University,
Masan,, Kyungnam 631-701, Korea
jongkyuk@kyungnam.ac.kr
Department of
Mathematics, Dongeui University,
Pusan 614-714, Korea
sskim@dongeui.ac.kr
Abstract:
Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [a, b].
Paper's Title:
Orthogonality and ε-Orthogonality in Banach Spaces
Author(s):
H. Mazaheri and S. M. Vaezpour
Faculty of Mathematics, Yazd University, Yazd, Iran
Abstract:
A concept of orthogonality on normed linear space was introduced by Brickhoff,
also the concept of ε-orthogonality was introduced by Vaezpour. In this note, we will consider the relation between these concepts and the dual of
X. Also some results on best coapproximation will be obtained.
Paper's Title:
Linearly Transformable Minimal Surfaces Author(s):
Harold R. Parks and Walter B. Woods
vaezpour@yazduni.ac.ir
hmazaheri@yazduni.ac.ir
2: Paper Source
PDF document
Department of Mathematics,
Oregon State University,
Corvallis, Oregon 97331--4605,
USA
parks@math.oregonstate.edu
URL: http://www.math.oregonstate.edu/people/view/parks/
Abstract:
We give a complete description of a nonplanar minimal surface in R3 with the surprising property that the surface remains minimal after mapping by a linear transformation that dilates by three distinct factors in three orthogonal directions. The surface is defined in closed form using Jacobi elliptic functions.
Paper's Title:
Differentiability of
Distance Functions in p-Normed Spaces
Author(s):
M. S. Moslehian, A. Niknam, S. Shadkam Torbati
Department of Pure Mathematics,
Centre of Excellence in Analysis on Algebraic Structures (CEAAS),,
Ferdowsi University of Mashhad,
P. O. Box
1159, Mashhad,
Iran
moslehian@ferdowsi.um.ac.ir
niknam@math.um.ac.ir
shadkam.s@wali.um.ac.ir
Abstract:
The farthest point mapping in a p-normed space X is studied in virtue of the Gateaux derivative and the Frechet derivative. Let M be a closed bounded subset of X having the uniformly p-Gateaux differentiable norm. Under certain conditions, it is shown that every maximizing sequence is convergent, moreover, if M is a uniquely remotal set then the farthest point mapping is continuous and so M is singleton. In addition, a Hahn--Banach type theorem in $p$-normed spaces is proved.
Paper's Title:
Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results
Author(s):
Sever S. Dragomir1,2
1Mathematics,
College of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
https://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
On an Extension of Hilbert’s Integral Inequality with Some Parameters
Author(s):
Bicheng Yang
Department of
Mathematics, Guangdong Education College, Guangzhou, Guangdong 510303, People’s
Republic of China.
bcyang@pub.guangzhou.gd.cn
URL:
http://www1.gdei.edu.cn/yangbicheng/index.html
Abstract:
In this paper, by introducing some parameters and estimating the
weight function, we give an extension of Hilbert’s integral inequality with a
best constant factor. As applications, we consider the equivalent form and some
particular results.
Paper's Title:
A relation between nuclear cones and full nuclear cones
Author(s):
G. Isac and A. B. Nemeth
Department of Mathematics,
Royal Military College of Canada,
P. O. Box 17000 STN Forces Kingston, Ontario,
Canada K7K 7B4.
isac-g@rmc.ca
Faculty of Mathematics and Computer Science,
Babes-Bolyai University,
3400 Cluj-Napoca,
Romania.
nemab@math.ubbcluj.ro
Abstract:
The notion of nuclear cone in locally convex spaces corresponds to the notion of well based cone in normed spaces. Using the bipolar theorem from locally convex spaces it is proved that every closed nuclear cone is a full nuclear cone. Thus every closed nuclear cone can be associated to a mapping from a family of continuous seminorms in the space to the topological dual of the space. The relation with Pareto efficiency is discussed.
Paper's Title:
A Strengthened Hardy-Hilbert's Type Inequality
Author(s):
Weihong Wang and Bicheng Yang
Department of Mathematics, Guangdong Education Institute,
Guangzhou, Guangdong 520303,
People's Republic Of China
wwh@gdei.edu.cn
bcyang@pub.guangzhou.gd.cn
URL: http://www1.gdei.edu.cn/yangbicheng/index.html
Abstract:
By using the improved Euler-Maclaurin's summation formula and
estimating the weight coefficient, we give a new strengthened
version of the more accurate Hardy-Hilbert's type inequality. As
applications, a strengthened version of the equivalent form is
considered.
Paper's Title:
A New Step Size Rule in Noor's Method for Solving General Variational Inequalities
Author(s):
Abdellah Bnouhachem
School of Management Science and Engineering, Nanjing University,
Nanjing, 210093
P.R. China.
babedallah@yahoo.com
Abstract:
In this paper, we propose a new step size rule in Noor's method
for solving general
variational inequalities. Under suitable conditions, we prove that the
new method is globally convergent. Preliminary numerical
experiments are included to illustrate the advantage and
efficiency of the proposed method.
Paper's Title:
The Riemann-Stieltjes Integral on Time Scales
Author(s):
D. Mozyrska, E. Pawłuszewicz, D. Torres
Faculty Of Computer Science,
Białystok University Of Technology,
15-351 Białystok,
Poland
d.mozyrska@pb.edu.pl
Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
ewa@ua.pt
Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
delfim@ua.pt
Abstract:
We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given
Paper's Title:
An Lp Inequality for `Self-Reciprocal' Polynomials. II
Author(s):
M. A. Qazi
Department of Mathematics,
Tuskegee University,
Tuskegee, Alabama 36088
U.S.A.
Abstract:
The main result of this paper is a sharp integral mean inequality for the derivative of a `self-reciprocal' polynomial.
Paper's Title:
Some Inequalities Concerning Derivative and Maximum Modulus of Polynomials
Author(s):
N. K. Govil, A. Liman and W. M. Shah
Department of Mathematics & Statistics,
Auburn University, Auburn,
Alabama 36849-5310,
U.S.A
Department of Mathematics,
National Institute of Technology,
Srinagar, Kashmir,
India - 190006
Department of Mathematics,
Kashmir University,
Srinagar, Kashmir,
India - 190006
govilnk@auburn.edu
abliman22@yahoo.com
wmshah@rediffmail.com
Abstract:
In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the inequalities obtained are sharp.
Paper's Title:
Certain Compact Generalizations of Well-Known Polynomial Inequalities
Author(s):
N. A. Rather and Suhail Gulzar
Department of Mathematics,
University of Kashmir, Hazratbal Srinagar-190006,
India.
Abstract:
In this paper, certain sharp compact generalizations of well-known Bernstien-type inequalities for polynomials, from which a variety of interesting results follow as special cases, are obtained.
Paper's Title:
Cubic Alternating Harmonic Number Sums
Author(s):
Anthony Sofo
Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
E-mail:
Anthony.Sofo@vu.edu.au
Abstract:
We develop new closed form representations of sums of cubic alternating harmonic numbers and reciprocal binomial coefficients. We also identify a new integral representation for the ζ (4) constant.
Paper's Title:
A Self Adaptive Method for Solving Split Bilevel Variational Inequalities Problem in Hilbert Spaces
Author(s):
Francis Akutsah1, Ojen Kumar Narain2, Funmilayo Abibat Kasali3 Olawale Kazeem Oyewole4 and Akindele Adebayo Mebawondu5
1School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
2School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za
3Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: fkasali@mtu.edu.ng
4Technion-Israel
Institute of Technology.
E-mail: 217079141@stu.ukzn.ac.za,
oyewoleolawalekazeem@gmail.co
5School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: dele@aims.ac.za
Abstract:
In this work, we study the split bilevel variational inequality problem in two real Hilbert spaces. We propose a new modified inertial projection and contraction method for solving the aforementioned problem when one of the operators is pseudomonotone and Lipschitz continuous while the other operator is α-strongly monotone. The use of the weakly sequential continuity condition on the Pseudomonotone operator is removed in this work. A Strong convergence theorem of the proposed method is proved under some mild conditions. In addition, some numerical experiments are presented to show the efficiency and implementation of our method in comparison with other methods in the literature in the framework of infinite dimensional Hilbert spaces. The results obtained in this paper extend, generalize and improve several.
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