15 research outputs found
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
On common fixed points approximation of countable families of certain multi-valued maps in hilbert spaces.
Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2017.Fixed point theory and its applications have been widely studied by many researchers.
Di erent iterative algorithms have been used extensively to approximate solutions of xed
point problems and other related problems such as equilibrium problems, variational in-
equality problems, optimization problems and so on. In this dissertation, we rst introduce
an iterative algorithm for nding a common solution of multiple-set split equality mixed
equilibrium problem and xed point problem for in nite families of generalized ki-strictly
pseudo-contractive multi-valued mappings in real Hilbert spaces. Using our iterative algo-
rithm, we obtain weak and strong convergence results for approximating a common solution
of multiple-set split equality mixed equilibrium problem and xed point problem. As ap-
plication, we utilize our result to study the split equality mixed variational inequality and
split equality convex minimization problems .
Also, we present another iterative algorithm that does not require the knowledge of the oper-
ator norm for approximating a common solution of split equilibrium problem and xed point
problem for in nite family of multi-valued quasi-nonexpansive mappings in real Hilbert
spaces. Using our iterative algorithm, we state and prove a strong convergence result for
approximating a common solution of split equilibrium problem and xed point problem
for in nite family of multi-valued quasi-nonexpansive mappings in real Hilbert spaces. We
apply our result to convex minimization problem and also present a numerical example
On some Mann's type iterative algorithms
AbstractFirst we present some interesting variants of Mann's method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions on the coefficients
A study of optimization and fixed point problems in certain geodesic metric spaces.
Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF
A study of optimization problems and fixed point iterations in Banach spaces.
Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF
Iterative schemes for approximating common solutions of certain optimization and fixed point problems in Hilbert spaces.
Masters Degree. University of KwaZulu-Natal, Durban.In this dissertation, we introduce a shrinking projection method of an inertial type with
self-adaptive step size for finding a common element of the set of solutions of Split Gen-
eralized Equilibrium Problem (SGEP) and the set of common fixed points of a countable
family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step
size incorporated helps to overcome the difficulty of having to compute the operator norm
while the inertial term accelerates the rate of convergence of the propose algorithm. Under
standard and mild conditions, we prove a strong convergence theorem for the sequence
generated by the proposed algorithm and obtain some consequent results. We apply our
result to solve Split Mixed Variational Inequality Problem (SMVIP) and Split Minimiza-
tion Problem (SMP), and present numerical examples to illustrate the performance of
our algorithm in comparison with other existing algorithms. Moreover, we investigate the
problem of finding common solutions of Equilibrium Problem (EP), Variational Inclusion
Problem (VIP)and Fixed Point Problem (FPP) for an infinite family of strict pseudo-
contractive mappings. We propose an iterative scheme which combines inertial technique
with viscosity method for approximating common solutions of these problems in Hilbert
spaces. Under mild conditions, we prove a strong theorem for the proposed algorithm and
apply our results to approximate the solutions of other optimization problems. Finally,
we present a numerical example to demonstrate the efficiency of our algorithm in comparison with other existing methods in the literature. Our results improve and complement
contemporary results in the literature in this direction
A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems
We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature