Strong convergent result for monotone inclusion and fixed point problems in hilbert spaces

Abstract

Our purpose in this paper is to propose an iterative algorithm to find a common element of the fixed points set of an infinite family of k-demicontractive mappings which is also a zero of the sum of two monotone operators, with one of the operators being maximal monotone and the other inverse-strongly monotone. We obtain strong convergence result of the sequence of iterates generated by our algorithm in a Hilbert space setting. Our result complements and generalizes some related results in literature.