Strong Convergence Algorithms Involving Two Iterative Sequences for Solving Common Fixed Point Problems With an Application

The goal of this study is dedicated to the research on the fixed point iterative algorithm for solving the common fixed point problems in Hilbert spaces. In this study, we first propose the hybrid and shrinking projection algorithms of two different nonexpansive mappings for a class of algorithms with two iterative sequences to solve the common fixed point problem, and we establish the strong convergence theorems of the proposed algorithms. Then, we demonstrate the iterative performance of the proposed algorithm through some numerical examples.