The resolvent operator techniques with perturbations for finding zeros of maximal monotone operator and fixed point problems in Hilbert spaces

Pongsakorn Sunthrayuth, Poom Kumam

Abstract

In this paper, we introduce iterative schemes with perturbations forfinding zeros of the sum of two monotone operators and a fixed pointproblem of a nonexpansive mapping in Hilbert spaces. We prove astrong convergence theorem of the proposed iterative schemes undersome certain conditions. Furthermore, we also apply our results tosolving the variational inequality and equilibrium problems. Theresults obtained in this paper are improve and generalize many knownrecent results in this field.