The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

Abstract

The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set $\Xi$ of a general system of variational inequalities, the solution set $\mathrm{\Gamma }$ of a split feasibility problem, and the fixed point set $\mathrm{Fix}(S)$ of a strictly pseudocontractive mapping $S$ in the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of $\text{Fix}(S)\cap \mathrm{\Xi }\cap \mathrm{\Gamma }$ under mild conditions.