Paper's Title:

On General Class of Nonlinear Contractive Maps and their Performance Estimates

Author(s):

Olalekan Taofeek Wahab and Salaudeen Alaro Musa

Department of Mathematics and Statistics
Kwara State University, Malete
P. M. B. 1530 Ilorin,
Nigeria.
E-mail: taofeek.wahab@kwasu.edu.ng

Abstract:

This paper considers two independent general class of nonlinear contractive maps to study the existence properties of nonlinear operators with prior degenerate. The existence properties are proved in the framework of approximate fixed points with the imposition of the general class of contractive conditions in metrical convex spaces without emphasis on completeness or compactness. For computational purposes, the performance estimates and the sensitivity dependence of these conditions are obtained for the Picard operator. Practical examples are also considered to justify the validity of the conditions. The results ensure no term is lost in the operators with prior degenerate and the conditions are strictly larger class when compare with others in the literature.

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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