Variational Inequality Problem Involving Multivalued Nonexpansive Mapping in CAT(0) Spaces - Gursoy, Faik; Hacioglu, Emirhan; Karakaya, Vatan; Milovanovic, Gradimir, V; Uddin, Izhar (SPRINGER BASEL AG, 2022)
In this paper, we introduce a new type of variational inequality problem (VIP) involving nonself multivalued mappings in CAT(0) spaces. We show that this VIP problem admit a solution under suitable conditions. We also perform the convergence analysis of introduced VIP via proximal multivalued Picard-S iteration. We finish our paper with some convergence theorems for new iteration scheme and system of variational inequalities associated with finite family of nonself multivalued nonexpansive mappings.
Keywords: Variational inequality; iterative methods; nonexpansive mapping; convergence analysis; multivalued mappings; CAT(0) spaces; Delta-convergence; FIXED-POINT; CONVERGENCE; THEOREMS; MANN; Mathematics