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

Demonstratio mathematica

article

Kazeem O. Aremu¹  Chinedu Izuchukwu¹  Godwin C. Ugwunnadi²  Oluwatosin T. Mewomo¹ 

[1] School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal;Department of Mathematics, University of Eswatini

关键词: demimetric mappings;    minimization problem;    CAT(0) spaces;    fixed point problem;   

DOI  :  10.1515/dema-2018-0022

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY