A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space

Abstract

The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.

Keywords

• equilibrium problems
• monotone bifunctions
• variational inequalities
• convex feasibility problems
• minimization problems
• viscosity iterations
• CAT(0) space