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

Aremu K. O., Izuchukwu C., Ugwunnadi G. C., Mewomo O. T.

Demonstratio Mathematica

2018

Vol. 51, nr 1

277--294

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.