# Iterative approximation of solutions of some optimization problems in Banach spaces.

## Date

2018

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## Abstract

Let C be a nonempty closed convex subset of a q-uniformly smooth Banach space X which
admits a weakly sequentially continuous generalized duality mapping. In this dissertation,
we study the approximation of the zero of a strongly accretive operator A : X ! X
which is also a xed point of a k-strictly pseudo-contractive self mapping T of C: Also,
we introduce a U-mapping for nite family of mixed equilibrium problems involving
relaxed monotone operators. We prove a strong convergence theorem for nding a common
solution of nite family of these equilibrium problems in a uniformly smooth and strictly
convex Banach space. We present some applications of this theorem and a numerical
example. Furthermore, due to the faster rate of convergence of inertial type algorithm, we
propose an inertial type iterative algorithm and prove a weak convergence theorem of the
scheme to a solution of split variational inclusion problems involving accretive operators in
Banach spaces. We give some applications and a numerical example to show the relevance
of our result. Our results in this dissertation extend and improve some recent results in
the literature.

## Description

Master’s Degree. University of KwaZulu-Natal, Durban.