Algorithms for Solution of Fixed Point and Equilibrium Problems in a Banach Space

Enyinnaya Ekuma-Okereke and Abel Okojunu
Keywords: Bregman strongly nonexpansive, equilibrium problem, Bregman Projection, inertial component, strong convergence.
Tropical Journal of Science and Technology 2020 1(1), 105-123. Published: June 29, 2020


Abstract

This paper considers two new algorithms of inertial hybrid type for finding common fixed point problems involving finite family of Bregman strongly nonexpansive mappings which also finds the common solution of finite system of equilibrium problems. We prove strong convergence results for the constructed algorithms. We apply our algorithms in finding common solutions of convex feasibility problems. We also demonstrate numerical experiments to verify the theoretical assertions and properties. We observe the performance results of our algorithms with the inertial component known to improve and speed up convergence. From the generated data, we observed that the solutions for our methods are significantly similar for any well-chosen standard tolerance rate. The results obtained further demonstrate the effectiveness, applicability and convergence of our algorithms in Banach spaces. Our results significantly improves, extends many cited works in the literature.