15 research outputs found

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

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    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.

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    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

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    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.

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

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

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    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.

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    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

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    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
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