Iterative methods for common best proximity point problems and quasi-variational inclusion problems in Banach Spaces

Abstract

The first aim of this thesis is to introduce and study new algorithms for finding a common best proximity point for two generalized nonexpansive type mappings. Weak and strong convergence theorems of the proposed algorithms are established under some suitable conditions and some numerical examples supporting these main results are also presented. The next aim of this thesis is to present a new algorithm for solving a system of quasi-variational inclusion problems and common fixed point problems in a Banach space. We prove a strong convergence theorem of the proposed algorithm under some control conditions. Furthermore, some applications for variational inequality problems, convex minimization problems and equilibrium problems are also given. Finally, we also perform some numerical experiments to the image restoration problems by utilizing the proposed algorithm. The presented results in this thesis extend and improve many well-known in the literature.