Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi--Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors

Iterative algorithms for approximating solutions of variational inequality problems and monotone inclusion problems.

Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban, 2017.In this work, we introduce and study an iterative algorithm independent of the operator norm for approximating a common solution of split equality variational inequality prob- lem and split equality xed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality variational inequality problem and the set of solutions of a split equality xed point problem for demicontractive mappings in real Hilbert spaces. We then considered nite families of split equality variational inequality problems and proposed an iterative algorithm for approximating a common solution of this problem and the multiple-sets split equality xed point problem for countable families of multivalued type-one demicontractive-type mappings in real Hilbert spaces. A strong convergence re- sult of the sequence generated by our proposed algorithm to a solution of this problem was also established. We further extend our study from the frame work of real Hilbert spaces to more general p-uniformly convex Banach spaces which are also uniformly smooth. In this space, we introduce an iterative algorithm and prove a strong convergence theorem for approximating a common solution of split equality monotone inclusion problem and split equality xed point problem for right Bregman strongly nonexpansive mappings. Finally, we presented numerical examples of our theorems and applied our results to study the convex minimization problems and equilibrium problems

Iterative algorithms for solutions of nonlinear equations in Banach spaces.

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

ON APPROXIMATION OF FIXED POINTS OF MEAN NONEXPANSIVE MAPPINGS IN CAT(0) SPACES

A new iterative algorithm for approximating fixed pointsof mean nonexpansive mappings in CAT(0) spaces is introduced. As a result, a weak convergence theorem is established.The result we obtain improves and extends several recent results in the literature. Finally, some numerical examples are presentedto illustrate the main result and to compare the new algorithm with some existing ones

Iterative algorithms for approximating solutions of some optimization problems in Hadamard spaces.

Masters Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF.Some text in red

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

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