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

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.

Iterative approximation of common fixed points of two nonself asymptotically nonexpansive mappings in CAT(0) spaces with numerical examples

“…As a consequence of this inequality, CAT(0) spaces posses many interesting properties such as non‐convex function (resp. set) can be viewed as convex function (rep. set) [19]. Some brilliant known results in $$$ \mathrm{CAT}(0) $$$ spaces can be found in previous studies [20–27] and references therein.…”