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:

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.

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