Weak Convergence Theorem for Infinite Families of Nonlinear Mappings in Banach Spaces (Study on Nonlinear Analysis and Convex Analysis)

In this article, we prove a weak convergence theorem of Mann's type iteration for infinite families of extended generalized hybrid mappings in a Banach space satisfying Opial's condition. This theorem solves a problem posed by Hojo and Takahashi [8]. Using this result, we get well-known and new weak convergence theorems in a Banach space. In particular, we obtain a weak convergence theorem of Mann's type iteration for finite families of extended generalized hybrid mappings in a Banach space

On Best Proximity Point Theorems and Fixed Point Theorems for -Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent -hybrid -cyclic self-mappings relative to a Bregman distance , associated with a Gâteaux differentiable proper strictly convex function in a smooth Banach space, where the real functions and quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping. Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings

Iterative methods for approximating solutions of certain optimization problems and fixed points problems.

Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2017.Abstract available in PDF file

A study of optimization problems and fixed point iterations in Banach spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF

Nonlinear Analysis and Optimization with Applications

Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world

A study of optimization and fixed point problems in certain geodesic metric spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF

Proximal-type algorithms for split minimization problem in P-uniformly convex metric spaces

In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces. We also analyse asymptotic behaviour of the sequence generated by Halpern-type proximal point algorithm and extend it to approximate a common solution of a finite family of minimization problems in the setting of complete p-uniformly convex metric spaces. Furthermore, numerical experiments of our algorithms in comparison with other algorithms are given to show the applicability of our results.http://link.springer.com/journal/110752019-11-19hj2018Mathematics and Applied Mathematic