


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:
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,
H4010 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 2homogeneous 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:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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 realvalued 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:
On Trigonometric Approximation of Continuous Functions by Deferred Matrix Means
Author(s):
Xhevat Zahir Krasniqi
Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë
10000,
Republic of Kosovo.
Email: xhevat.krasniqi@unipr.edu
URL:
https://staff.unipr.edu/profile/xhevatkrasniqi
Abstract:
In this paper, for the first time, we introduce the deferred matrix means which contain the wellknown generalized deferred Nörlund, deferred Nörlund, deferred Riesz, deferred Cesàro means introduced earlier by others, and a new class of sequences (predominantly a wider class than the class of Head Bounded Variation Sequences). In addition, using the deferred matrix means of Fourier series of a continuous function, we determine the degree of approximation of such function via its modulus of continuity and a positive mediate function.
Paper's Title:
Inequalities for Discrete FDivergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated fdivergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of KullbackLeibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the fdivergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
Necessary and Sufficient Conditions for Uniform Convergence and Boundedness of a General Class of Sine Series
Author(s):
Laszlo Leindler
Bolyai Institute, University of Szeged,
Aradi Vértanúk tere 1,
H6720 Szeged,
Hungary.
leindler@math.uszeged.hu
Abstract:
For all we know theorems pertaining to sine series with coefficients from the class γGBVS give only sufficient conditions. Therefore we define a subclass of γGBVS in order to produce necessary and sufficient conditions for the uniform convergence and boundedness if the coefficients of the sine series belong to this subclass; and prove two theorems of this type.
Paper's Title:
On the Degree of Approximation of Continuous Functions that Pertains to the SequenceToSequence Transformation
Author(s):
Xhevat Z. Krasniqi
University of Prishtina,
Department of Mathematics and Computer Sciences,
5
Mother Teresa Avenue, Prishtinë, 10000,
Republic of Kosovo.
Abstract:
In this paper we prove analogous theorems like Leindler's 3 using the socalled Atransform of the Btransform of the partial sums of Fourier series. In addition, more than two such transforms are introduced and for them analogous results are showed as well.
Paper's Title:
Sharp L^{p} Improving Results for Singular Measures on C^{n+1}
Author(s):
E. Ferreyra, M. Urciuolo
FaMAFCIEM,
Universidad Nacional de CórdobaConicet,
Ciudad Universitaria, 5000 Córdoba,
Argentina
eferrey@famaf.unc.edu.ar
urciuolo@famaf.unc.edu.ar
Abstract:
For j=1,...,n, let Ω_{j} be open sets of the complex plane and let φ_{j} be holomorphic functions on Ω_{j} such that φ_{j}^{''} does not vanish identically on Ω_{j.} We consider φ(z_{1},...,z_{n}) =φ_{1}(z_{1}) +...+φ_{n}(z_{n}). We characterize the pairs (p,q) such that the convolution operator with the surface measure supported on a compact subset of the graph of φ is pq bounded.
Paper's Title:
New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
Author(s):
S. S. Dragomir
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
Abstract:
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.
Paper's Title:
Integrability of Sine and Cosine Series Having Coefficients of a New Class
Author(s):
L. Leindler
Bolyai Institute,
University of Szeged, Aradi Vértanúk Tere 1, H6720 Szeged, Hungary
leindler@math.uszeged.hu
Abstract:
Some integrability theorems or only their sufficient part are generalized such that the coefficients of the sine and cosine series belong to a new class of sequences being wider than the class of sequences of rest bounded variation, which itself is a generalization of the monotone decreasing sequences, but a subclass of the almost monotone decreasing sequences. It is also verified that the new class of sequences and the class of almost monotone decreasing sequences are not comparable.
Paper's Title:
Refinement Inequalities Among Symmetric Divergence Measures
Author(s):
Inder Jeet Taneja
Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040900
Florianópolis, Sc, Brazil
taneja@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~taneja
Abstract:
There are three classical divergence measures in the literature on information theory and statistics, namely, JeffryesKullbackLeiber’s Jdivergence, SibsonBurbeaRao’s Jensen Shannon divegernce and Taneja’s arithemtic  geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ^{2}−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.
Paper's Title:
On a Method of Proving the HyersUlam Stability of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchorąźych 2,
30084 Kraków,
Poland
jbrzdek@ap.krakow.pl
Abstract:
We show that generalizations of some (classical) results on the HyersUlam 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:
On a Subclass of Uniformly Convex Functions Defined by the DziokSrivastava Operator
Author(s):
M. K. Aouf and G. Murugusundaramoorthy
Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com
School of Science and Humanities, VIT University
Vellore  632014,
India.
gmsmoorthy@yahoo.com
Abstract:
Making use of the DziokSrivastava operator, we define a new subclass T^{l}_{m}([α_{1}];α,β) of uniformly convex function with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of closetoconvexity, starlikeness and convexity for functions belonging to the class T^{l}_{m}([α_{1}];α,β) . We consider integral operators associated with functions belonging to the class H^{l}_{m}([α_{1}];α,β) defined via the DziokSrivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class T^{l}_{m}([α_{1}];α,β) and we obtain properties associated with generalized fractional calculus operators.
Paper's Title:
A Sum Form Functional Equation and Its Relevance in Information Theory
Author(s):
Prem Nath and Dhiraj Kumar Singh
Department of Mathematics
University of Delhi
Delhi  110007
India
pnathmaths@gmail.com
dksingh@maths.du.ac.in
Abstract:
The general solutions of a sum form functional equation containing four unknown mappings have been investigated. The importance of these solutions in relation to various entropies in information theory has been emphasised.
Paper's Title:
Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces
Author(s):
S. S. Dragomir
School of Engineering and Science
Victoria University, PO 14428
Melbourne City MC,
Victoria 8001,
Australia
sever.dragomir@vu.edu.au
URL: http://www.staff.vu.edu.au/RGMIA/dragomir/
Abstract:
Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are surveyed.
Paper's Title:
Stability of Almost Multiplicative Functionals
Author(s):
Norio Niwa, Hirokazu Oka, Takeshi Miura and SinEi Takahasi
Faculty of Engineering, Osaka ElectroCommunication University,
Neyagawa 5728530,
Japan
Faculty of Engineering, Ibaraki University,
Hitachi 3168511,
Japan
Department of Applied Mathematics and Physics, Graduate School of
Science and Engineering,
Yamagata University,
Yonezawa 9928510
Japan
oka@mx.ibaraki.ac.jp
miura@yz.yamagatau.ac.jp
sinei@emperor.yz.yamagatau.ac.jp
Abstract:
Let δ and p be nonnegative 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 HyersUlamRassias 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:
Fejértype Inequalities
Author(s):
Nicuşor Minculete and FlaviaCorina Mitroi
"Dimitrie Cantemir" University,
107 Bisericii Române Street, Braşov, 500068,
România
minculeten@yahoo.com
University of Craiova, Department of Mathematics,
Street A. I. Cuza
13, Craiova, RO200585,
Romania
fcmitroi@yahoo.com
Abstract:
The aim of this paper is to present some new Fejértype results for convex functions. Improvements of Young's inequality (the arithmeticgeometric mean inequality) and other applications to special means are pointed as well.
Paper's Title:
On Convergence Theorems of an Implicit Iterative Process with Errors for a Finite Family of Asymptotically quasi Inonexpansive Mappings
Author(s):
Farrukh Mukhamedov and Mansoor Saburov
Department of Computational & Theoretical
Sciences,
Faculty of Sciences, International Islamic University Malaysia,
P.O. Box, 141, 25710, Kuantan,
Malaysia
Abstract:
In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {T_{j}}^{N}_{i=1} of asymptotically quasi I_{j}nonexpansive mappings as well as a family of {Ij}^{N}_{j=1} of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existing literature.
Paper's Title:
Some Double λConvergent Sequence Spaces Over nNormed Spaces
Author(s):
Kuldip Raj, Renu Anand and Seema Jamwal
School of Mathematics,
Shri Mata Vaishno Devi University Katra182320,
Jammu and Kashmir,
India.
Email: kuldipraj68@gmail.com, renuanand71@gmail.com, seemajamwal8@gmail.com
Abstract:
In this paper we introduce some double generalized λconvergent sequence spaces over nnormed spaces defined by MusielakOrlicz function M = (M_{k,l}). We also made an attempt to study some topological and algebraic properties of these sequence spaces.
Paper's Title:
HermiteHadamardFejer Type Inequalities for Harmonically sconvex Functions via Fractional Integrals
Author(s):
İmdat İşcan, Mehmet Kunt
Department of Mathematics,
Faculty of Sciences and Arts,
Giresun University, Giresun,
Turkey.
Email: imdat.iscan@giresun.edu.tr
Department of Mathematics,
Faculty of Sciences,
Karadeniz Technical University,
61080, Trabzon,
Turkey.
Email:
mkunt@ktu.edu.tr
Abstract:
In this paper, some HermiteHadamardFejer type integral inequalities for harmonically sconvex functions in fractional integral forms have been obtained.
Paper's Title:
Some Grüss Type Inequalities in Inner Product Spaces
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir
Abstract:
Some inequalities in inner product spaces that provide upper bounds for the quantities
and ,
where e,f ∈ H with and x,y are vectors in H satisfying some appropriate assumptions are given. Applications for discrete and integral inequalities are provided as well.
Paper's Title:
C*valued metric projection and MoorePenrose inverse on Hilbert C*modules
Author(s):
M. Eshaghi Gordji, H. Fathi and S.A.R. Hosseinioun
Department of Mathematics,
Semnan University, P.O. Box 35195363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
Email: Madjid.Eshaghi@gmail.com
Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
Email: Hedayat.fathi@yahoo.com
Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
Email: shossein@uark.net
Abstract:
Let t be a regular operator between Hilbert C^{*}modules and t^{†} be its MoorePenrose inverse. We give some characterizations for t^{†} based on C^{*}valued metric projection. MoorePenrose inverse of bounded operators and elements of a C^{*}algebra is studied as a special case.
Paper's Title:
Relation Between The Set Of Nondecreasing Functions And The Set Of Convex Functions
Author(s):
Qefsere Doko Gjonbalaj and Luigj Gjoka
Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova
Email:
qefsere.gjonbalaj@unipr.edu
Department of Engineering Mathematics,
Polytechnic University of Tirana, Tirana,
Albania.
Email: luigjgjoka@ymail.com
Abstract:
In this article we address the problem of integral presentation of a convex function. Let I be an interval in R. Here, using the Riemann or Lebesgue’s integration theory, we find the necessary and sufficient condition for a function f: I→ R to be convex in I.
Paper's Title:
Cubic Alternating Harmonic Number Sums
Author(s):
Anthony Sofo
Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
Email:
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:
Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
College of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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:
Estimates of Norms on Krein Spaces
Author(s):
Satheesh K. Athira, P. Sam Johnson and K. Kamaraj
Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
Email: athirachandri@gmail.com
Department of Mathematical and
Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
Email:sam@nitk.edu.in
Department of Mathematics,
University College of Engineering Arni,
Anna University, Arni 632 326,
India.
Email: krajkj@yahoo.com
Abstract:
Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and a few results in Bognar's paper are generalized.
Paper's Title:
Trace Inequalities for Operators in Hilbert Spaces: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
School of Engineering
& Science
Victoria University,
PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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:
In this paper we survey some recent trace inequalities for operators in Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's inequalities and the reverses of Schwarz inequality known in the literature as Cassels' inequality and ShishaMond's inequality. Applications for some functionals that are naturally associated to some of these inequalities and for functions of operators defined by power series are given. Further, various trace inequalities for convex functions are presented including refinements of Jensen inequality and several reverses of Jensen's inequality. HermiteHadamard type inequalities and the trace version of Slater's inequality are given. Some Lipschitz type inequalities are also surveyed. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well.
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