ITERATIVE METHOD FOR SOLVING QUASI-EQUILIBRIUM PROBLEMS AND ZERO POINT PROBLEM IN HADAMARD SPACES

Abstract

In this paper, we propose a new iterative algorithm for finding a common elementof the set of solutions of the quasi-equilibrium problem and a common zero of a finite familyof monotone operators in Hadamard spaces. We obtain weak convergence of the sequence to a solution of the quasi-equilibrium problem and a common zero of a finite family of monotoneoperators under some mild assumptions. Then we show strong convergence of the generated sequence to a solution of the problem by imposing some additional conditions. Finally, anumerical experiment is reported to illustrate the eciency of the proposed algorithm.