A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators

Abstract

The purpose of this paper is to introduce a new iterative scheme for finding a commonelement of the set of solutions of generalized mixed equilibrium problems, the set of solutions ofvariational inequality problems, the zero point of maximal monotone operators, and the set of twocountable families of quasi-$\varphi$-nonexpansive mappings in Banach spaces. Moreover, the strong convergencetheorems of this method are established under the suitable conditions of the parameter imposedon the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotoneoperators and complementarity problems. Our results presented in this paper improve and extendthe recently results by many others.