Modified Proximal Point Methods Involving Quasi-pseudocontractive Mappings in Hadamard Spaces

Abstract

In this paper, we propose two new proximal point methods involving quasi-pseudocontractive mappings in Hadamard spaces. We prove that the first method converges strongly to a common solution of a finite family of minimization problems and fixed point problem for a finite family of quasi-pseudocontractive mappings in an Hadamard space. We then extend this method to a more general method involving multivalued monotone operators to approximate the solution of monotone inclusion problem, which is an important optimization problem. We establish that this method converges strongly to a common zero of a finite family of multivalued monotone operators which is also a common fixed point of a finite family of quasi-pseudocontractive mappings in an Hadamard space. Furthermore, we provide various nontrivial numerical implementations of our method in Hadamard spaces (which are non-Hilbert) and compare them with some other recent methods in the literature.