(1) College of Statistics and Mathematics, Yunnan Uniersity of Finance and Economics, Kunming, 650221, P. R. China;(2) Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China
Abstract:
The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element
in the intersection of the set of common fixed points of an infinite family of quasi-ϕ-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational
inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly
smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem
(CFP) and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and
extend the corresponding results announced by many authors.