General viscosity iterative process for solving variational inclusion and fixed point problems involving multivalued quasi-nonexpansive and demicontractive operators with application

Modified Viscosity Iterative Algorithm for Solving Variational Inclusion and Fixed Point Problems in Real Hilbert Space

“…These investigations have built upon the concepts of viscosity solutions introduced by various researchers. (see e.g [6], [25], [5], [29], [23], [19], [28]).…”

“…Most recently, Sow [28] introduced and studied a new iterative algorithm and prove convergence theorems for variation inclusion problem (1.8) and fixed point problem involving multivalued demicontractive and quasi-nonexpansive mappings in Hilbert spaces. They defined the sequence…”

“…It is our purpose in this paper to construct a new iteration process, that modifies that of Sow [28] and prove that the corresponding sequence {x n } converges strongly to a common point of an inclusion problem and fixed point of a family of multivalued demicontractive and quasi-nonexpansive mappings in Hilbert spaces without any compactness. Our theorems generalize and extend that of Sow [28], and many other results in this directions.…”

“…Lemma 2.2. [28]. Let H be real Hilbert space and Λ : H → H be an α−inverse strongly monotone mapping.…”