Approximation of G-variational inequality problems and fixed-point problems of G-κ-strictly pseudocontractive mappings by an intermixed method endowed with a graph

Abstract

In this paper, we first study G-κ-strictly pseudocontractive mappings and we establish a strong convergence theorem for finding the fixed points of two G-κ-strictly pseudocontractive mappings, two G-nonexpansive mappings, and two G-variational inequality problems in a Hilbert space endowed with a directed graph without the Property G. Moreover, we prove an interesting result involving the set of fixed points of a G-κ-strictly pseudocontractive and G-variational inequality problem and if Λ is a G-κ-strictly pseudocontractive mapping, then $I-\Lambda $ I − Λ is a $G-\frac{(1-\kappa )}{2}$ G − ( 1 − κ ) 2 -inverse strongly monotone mapping, shown in Lemma 3.3. In support of our main result, some examples are also presented.