Strong convergence results for variational inequality problem in CAT(0) spaces

Abstract

The main purpose of this paper is to introduce and study a Halpern-type algorithm which comprises of a nonexpansive mapping and a finite family of inverse strongly monotone mappings recently introduced in CAT(0) spaces by Alizadeh-Dehghan-Moradlou [Fixed Point Theory 20(1)(2018)]. A strong convergence of the proposed algorithm to a common solution of a finite family of variational inequality problem and fixed point problem for a nonexpansive mapping is established in a complete CAT(0) space. Furthermore, we applied our results to approximate solutions of convex feasibility problems in complete CAT(0) spaces.