ITERATIVE ALGORITHM FOR APPROXIMATING SOLUTIONS OF SPLIT MONOTONE VARIATIONAL INCLUSION, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS IN REAL HILBERT SPACES

Abstract

The goal of this paper is to introduce a modified Halpern iterative algorithm for approximating solutions of split monotone variational inclusion, variational inequality and fixed point problems of an infinite families of multi-valued type-one demicontractive mappings in the framework of real Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution of split monotone variational inclusion, variational inequality problems and fixed point problem for countable family of multi-valued type-one demicontractive mappings. The iterative algorithm employed in this paper is designed in such a way that it does not require the knowledge of operator norm. Lastly, we give some consequences of our main result and give application of one of the consequences to split minimization problem. The result presented in this paper extends and generalizes some related results in literature.