On the proximal point algorithm and demimetric mappings in CAT(0) spaces

Abstract

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore,we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

Keywords

• demimetric mappings
• minimization problem
• CAT(0) spaces
• fixed point problem
• 47H06
• 47H09
• 47J05
• 47J25