Two new algorithms to solve the system of generalized mixed equilibrium and fixed point problems in Banach spaces

In this paper, we study the system of the generalized mixed equilibrium problems and the common fixed point problem of a finite family of quasi-Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi$$\end{document}-nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces. Using the shrinking projection method and the hybrid projection method, we propose and establish the strong convergence of two new iterative algorithms to find a common solution for this problem. Two numerical examples are also given for illustration.