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:

MSplit Equality for Monotone Inclusion Problem and Fixed Point Problem in Real Banach Spaces

Author(s):

^1,2Christian Chibueze Okeke, ³Abdumalik Usman Bello, ¹Chinedu Izuchukwu, and ¹Oluwatosin Temitope Mewomo

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: okekec@ukzn.ac.za
E-mail: izuchukwuc@ukzn.ac.za
E-mail: mewomoo@ukzn.ac.za

²DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-Mass)
Johannesburg,
South Africa.

³Federal University,
Dutsin-Ma, Katsina State,
Nigeria.
E-mail: uabdulmalik@fudutsinma.edu.ng

Abstract:

In this paper a new iterative algorithm for approximating a common solution of split equality monotone inclusion problem and split equality fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality monotone inclusion problem and the set of solutions of a split equality fixed point problem for right Bregman strongly nonexpansive mappings in the setting of p-uniformly convex Banach spaces which are also uniformly smooth. We also give some applications.

Paper's Title:

Some Convergence Results for  Jungck-Am Iterative Process In Hyperbolic Spaces

Author(s):

Akindele Adebayo Mebawondu and Oluwatosin Temitope Mewomo

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216028272@stu.ukzn.ac.za, mewomoo@ukzn.ac.za

Abstract:

In this paper, we introduce a new three steps iterative process called Jungck-AM iterative process and show that the proposed iterative process can be used to approximate fixed points of Jungck-contractive type mappings and Jungck-Suzuki type mappings. In addition, we establish some strong and Δ-convergence results for the approximation of fixed points of Jungck-Suzuki type mappings in the frame work of uniformly convex hyperbolic space. Furthermore, we show that the newly proposed iterative process has a better rate of convergence compare to the Jungck-Noor, Jungck-SP, Jungck-CR and some existing iterative processes in the literature. Finally, stability, data dependency results for Jungck-AM iterative process is established and we present an analytical proof and numerical examples to validate our claim.

Paper's Title:

A New Iterative Approximation of a Split Fixed Point Constraint Equilibrium Problem

Author(s):

Musa Adewale Olona¹, Adhir Maharaj² and Ojen Kumar Narain³

¹School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 219095783@stu.ukzn.ac.za

²Department of Mathematics,
Durban University of Technology, Durban,
South Africa.
E-mail: adhirm@dut.ac.za

³School 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 introduce an iterative algorithm for approximating an element in the solution set of the common split feasibility problem for fixed points of demimetric mappings and equilibrium problem for monotone mapping in real Hilbert spaces. Motivated by self-adaptive step size method, we incorporate the inertial technique to accelerate the convergence of the proposed method and establish a strong convergence of the sequence generated by the proposed algorithm. Finally, we present a numerical example to illustrate the significant performance of our method. Our results extend 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.

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