Strong convergence theorems for fixed point of multi-valued mappings in Hadamard spaces

Abstract

Abstract With the help of CN-inequality, we study fixed point of multi-valued mappings with closed bounded images and establish some strong convergence theorems involving a countable family of demicontractive mappings in Hadamard spaces. Furthermore, we use the established theorems to deduce some theorems involving a family of minimization problems, variational inequality problems, and monotone inclusion problems. We finally give examples to illustrate the results. The results obtained herein generalise some recent results in the literature.

Keywords

• Common fixed point
• Demiclosedness-type property
• Hadamard space
• Multi-valued demicontractive mappings
• Strong convergence
• Δ-convergence