DOI: 10.24193/fpt-ro.2023.1.13

Authors: C. Izuchukwu and O.T. Mewomo

Abstract: The main purpose of this paper is to introduce a viscosity-type proximal point algorithm for approximating a common solution of a finite family of equilibrium problems and fixed point problem for a certain class of nonspreading-type mappings recently introduced by Phuengrattana [Applied General Topology 18(2017), 117-129]. We further establish a strong convergence of our proposed algorithm to a common solution of a finite family of equilibrium problems which is also a fixed point of this class of mappings and a unique solution of some variational inequality problems in an Hadamard space. We also analyse the asymptotic behaviour of the sequence generated by a viscosity-type algorithm and extend the analysis to approximate a common solution of a finite family of equilibrium problems in an Hadamard space. Furthermore, we applied our results to solve some optimization problems in Hadamard spaces.

Key Words and Phrases: Equilibrium problems, monotone bifunctions, variational inequalities, nonspreading mappings, minimization problems, viscosity iterations, CAT(0) space.

2010 Mathematics Subject Classification: 47H09, 47H10, 49J20, 49J40.

Published on-line: February 1st, 2023.

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