A general iterative method for finding common fixed point of finite family of demicontractive mappings with accretive variational inequality problems in Banach spaces

Abstract

In this paper, we introduce a general iterative scheme for approximating a common fixed point of finite family of demicontractive mappings with accretive variational inequality problems in a real uniformly convex and uniformly smooth Banach space. We prove some strong convergence theorems under certain suitable conditions. Furthermore, we apply our results to solving convex minimization problems and linear inverse problem in real Hilbert spaces. Numerical example with graphical illustrations are also provided to show the efficiency of our algorithm. Our results improve and extend many other results in this direction in the literature.