The purpose of this article is to propose an iterative algorithm for finding an approximate solution of a split monotone variational inclusion problem for monotone operators which is also a solution of a fixed point problem for strictly pseudocontractive maps in real Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating a common solution of split monotone variational inclusion problem and fixed point problem for strictly pseudocontractive maps in the framework of real Hilbert spaces. Our result complements and extends some related results in literature.

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Abstract In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.