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 setΞof a general system of variational inequalities, the solution setΓof a split feasibility problem, and the fixed point setFix(S)of a strictly pseudocontractive mappingSin 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 ofFix(S)∩Ξ∩Γunder mild conditions.