Gursoy, FaikHacioglu, EmirhanKarakaya, VatanMilovanovic, Gradimir, VUddin, Izhar2024-06-122024-06-1220221422-63831420-9012https://doi.org/10.1007/s00025-022-01663-yhttps://hdl.handle.net/20.500.14551/24551In 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.en10.1007/s00025-022-01663-yinfo:eu-repo/semantics/closedAccessVariational InequalityIterative MethodsNonexpansive MappingConvergence AnalysisMultivalued MappingsCAT(0) SpacesDelta-ConvergenceFixed-PointConvergenceTheoremsMannArticle773Q1WOS:0007913741000032-s2.0-85129663457Q2