Variational Inequality Problem Involving Multivalued Nonexpansive Mapping in CAT(0) Spaces

GÜRSOY F., Hacioglu E., KARAKAYA V., Milovanovic G., Uddin I.

RESULTS IN MATHEMATICS, vol.77, no.3, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s00025-022-01663-y
  • Journal Name: RESULTS IN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Variational inequality, iterative methods, nonexpansive mapping, convergence analysis, multivalued mappings, CAT(0) spaces, Delta-convergence, FIXED-POINT, CONVERGENCE, THEOREMS, MANN
  • Yıldız Technical University Affiliated: Yes

Abstract

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.