Institute of Mathematics, University of Debrecen,
H-4010 Debrecen, Pf. 12,
Hungary
szaz@math.klte.hu

which are analytic in an open disk and study certain subclass of the class A, for which

has some property. Certain inclusion and the closure properties like convolution with convex univalent function etc. are studied.

Department of Mathematics
Chungnam National University
Daejeon, 305-764,
Republic of Korea
hmkim@cnu.ac.kr

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 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:

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:

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 Găvruţă for the G-type functional equation f(φ(x))=Γ(x)f(x)+ψ(x) and the stability in the sense of Ger for the functional equation of the form f(φ(x))=Γ(x)f(x). As a consequence, we obtain a stability results for G-function equation.

Paper's Title:

Iterative Approximation of Zeros of Accretive Type Maps, with Applications

Author(s):

Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo

African University of Science and Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: chinedu.ezea@gmail.com
E-mail: mrzzaka@yahoo.com

Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
E-mail: chinedu.ezea@gmail.com

Ebonyi State University,
Abakaliki,
Nigeria
E-mail: mrzzaka@yahoo.com

Abstract:

Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E→ E^* be the normalized duality map on E and let A:E^*→ E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)^-1(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u^* in (AJ)^-1(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, non-trivial examples of maps A for which AJ is accretive are presented..

Paper's Title:

Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces

Author(s):

¹U.A. Osisiogu, F.L. Adum, and ²C. Izuchukwu

¹Department of Mathematics and Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
E-mail: uosisiogu@gmail.com, adumson2@yahoo.com

²School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: izuchukwuc@ukzn.ac.za, izuchukwu_c@yahoo.com

Abstract:

The main purpose of this paper is to introduce a certain class of split generalized mixed equilibrium problem involving relaxed monotone mappings. To solve our proposed problem, we introduce an iterative algorithm and obtain its strong convergence to a solution of the split generalized mixed equilibrium problems in Hilbert spaces. As special cases of the proposed problem, we studied the proximal split feasibility problem and variational inclusion problem.

Paper's Title:

Existence of Solution of Differential and Riemann-Liouville Equation Via Fixed Point Approach in Complex Valued b-Metric Spaces

Author(s):

K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain

Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: dele@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: hammedabass548@gmail.com

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of C-class function in the framework of complex valued b-metric spaces. As an application, we establish the existence and uniqueness of a solution for Riemann-Liouville integral and ordinary differential equation in the framework of a complete complex valued b-metric spaces. The obtained results generalize and improve some fixed point results in the literature.

Paper's Title:

D-Iterative Method for Solving a Delay Differential Equation and a Two-Point Second-Order Boundary Value Problems in Banach Spaces

Author(s):

Francis Akutsah¹, Akindele Adebayo Mebawondu², Oluwatosin Babasola³, Paranjothi Pillay⁴ and Ojen Kumar Narain⁵

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. 
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

³Department of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath, BA2 7AY
UK.
E-mail: ob377@bath.ac.uk

⁴School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: pillaypi@ukzn.ac.za

⁵School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [2] and [3] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduced a modified approach using the D-iterative method to solve a two-point second-order boundary value problem, and also obtain the solution of a delay differential equations using the obtained results in this paper. The results presented in this paper do not only extend and improve the results obtained in [2, 3], it further extends and improve some existing results in the literature.

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.

Paper's Title:

On Stan Ulam and his Mathematics

Author(s):

Krzysztof Ciesielski and Themistocles M. Rassias

Mathematics Institute, Jagiellonian University,
Łjasiewicza 6, 30-348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr

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 a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains

Author(s):

Janusz Brzdęk

Department of Mathematics
 Pedagogical University Podchorąźych 2,
30-084 Kraków,
Poland
jbrzdek@ap.krakow.pl

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:

Fixed Points and Stability of the Cauchy Functional Equation

Author(s):

Choonkil Park and Themistocles M. Rassias

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:

An Efficient Modification of Differential Transform Method for Solving Integral and Integro-differential Equations

Author(s):

S. Al-Ahmad, Ibrahim Mohammed Sulaiman^*, and M. Mamat

Faculty of Informatics and Computing,
Universiti Sultan Zainal Abidin,
Terengganu, Besut Campus, 22200,
Malaysia.
E-mail: Alahmad.shadi@yahoo.com, ^*sulaimanib@unisza.edu.my, must@unisza.edu.my
 

Abstract:

In this paper, classes of integral and integro-differential equations are solved using a modified differential transform method. This proposed technique is based on differential transform method (DTM), Laplace transform (LT) procedure and Pad\'{e} approximants (PA). The proposed method which gives a good approximation for the true solution in a large region is referred to modified differential transform method (MDTM). An algorithm was developed to illustrate the flow of the proposed method. Some numerical problems are presented to check the applicability of the proposed scheme and the obtained results from the computations are compared with other existing methods to illustrates its efficiency. Numerical results have shown that the proposed MDTM method is promising compared to other existing methods for solving integral and integro-differential equations.

Paper's Title:

A Self-adaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces

Author(s):

F. U. Ogbuisi

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.

Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: ferdinard.ogbuisi@unn.edu.ng fudochukwu@yahoo.com

Abstract:

In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2-uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.

Paper's Title:

ψ(m,q)-Isometric Mappings on Metric Spaces

Author(s):

Sid Ahmed Ould Beinane, Sidi Hamidou Jah and Sid Ahmed Ould Ahmed Mahmoud

Mathematical Analysis and Applications, Mathematics Department, College of Science,
Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: beinane06@gmail.com

Department of Mathematics, College of Science Qassim University,
P.O. Box 6640, Buraydah 51452,
Saudi Arabia.
E-mail: jahsiidi@yahoo.fr

Mathematical Analysis and Applications,
Mathematics Department, College of Science, Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: sidahmed@ju.edu.sa, sidahmed.sidha@gmail.com

Abstract:

The concept of (m,p)-isometric operators on Banach space was extended to (m,q)-isometric mappings on general metric spaces in [6]. This paper is devoted to define the concept of ψ(m, q)-isometric, which is the extension of A(m, p)-isometric operators on Banach spaces introduced in [10]. Let T,ψ: (E,d) -> (E, d) be two mappings.
For some positive integer m and q ∈ (0,∞). T is said to be an ψ(m,q)-isometry, if for all  y,z ∈ E,

Paper's Title:

A New Method with Regularization for Solving Split Variational Inequality Problems in Real Hilbert Spaces

Author(s):

Francis Akutsah¹ and Ojen Kumar Narain²

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

Abstract:

In this paper, we introduce a new inertial extrapolation method with regularization for approximating solutions of split variational inequality problems in the frame work of real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the problem without using the conventional two cases approach. In addition, we present some numerical experiments to show the efficiency and applicability of the proposed method. The results obtained in this paper extend, generalize and improve several results in this direction.

Paper's Title:

Trace Inequalities for Operators in Hilbert Spaces: a Survey of Recent Results

Author(s):

Sever S. Dragomir^1,2

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: 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 Shisha-Mond'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. Hermite-Hadamard 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.

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.

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