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

Abstract

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 $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>I</mml:mi> <mml:mo>−</mml:mo> <mml:mi>Λ</mml:mi> </mml:math> is a $G-\frac{(1-\kappa )}{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>κ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> -inverse strongly monotone mapping, shown in Lemma 3.3. In support of our main result, some examples are also presented.