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

Iterative methods for solving split feasibility problem in Hilbert space

Based on the recent work of Wang et al. (2012), in this paper, we construct a new algorithm for solving split feasibility problem for the class of total quasi-asymptotically nonexpansive and uniformly τ−Lipschitzian mappings in Hilbert space and prove its strong convergence result. The result presented in this paper, not only extend the result of Wang et al. Wang et al. (2012), but also extend, improve and generalize several well-known results in the literature

On Asymptotically Quasi-φ-Nonexpansive Mappings in the Intermediate Sense

A projection iterative process is investigated for the class of asymptotically quasi-φ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common fixed points of a family of asymptotically quasi-φ-nonexpansive mappings in the intermediate sense are established in the framework of Banach spaces

Theory and Application of Fixed Point

In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications

Approximation methods for solutions of some nonlinear problems in Banach spaces.

Doctor of Philosophy in Mathematics. University of KwaZulu-Natal, Durban 2016.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