Iterative Methods of Weak and Strong Convergence Theorems for the Split Common Solution of the Feasibility Problems, Generalized Equilibrium Problems, and Fixed Point Problems

Abstract

The purpose of this paper is to introduce the extragradient methods for solving split feasibility problems, generalized equilibrium problems, and fixed point problems involved in nonexpansive mappings and pseudocontractive mappings. We establish the results of weak and strong convergence under appropriate conditions. As applications of our three main theorems, when the mappings and their domains take different types of cases, we can obtain nine iterative approximation theorems and corollas on fixed points, variational inequality solutions, and equilibrium points.

Tseng‐Type Algorithms for the Split Variational Inclusion

“…It should be pointed out that the operators h and φ in (10) were assumed to be inverse strongly monotone. e split variational inclusion (7) has been studied extensively, see [24,28,[30][31][32][33][34][35][36].…”