On modified proximal point algorithms for solving minimization problems and fixed point problems in CAT(<i>κ</i>) spaces

Abstract

In this paper, we show the existence of solutions of the convex minimization problems and common fixed problems in CAT(1) spaces under some mild conditions. For this, we propose the new modified the proximal point algorithm. Further, we give some applications for the convex minimization problem and the fixed point problem in CAT(kappa) spaces with the bounded positive real number kappa. Our results improve and generalize many recent important results in the literature.