On the Iterations of a Sequence of Strongly Quasi-nonexpansive Mappings with Applications

Abstract

In this paper, we study $\Delta$- convergence of iterations for a sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them in Hadamard spaces. Then, we give some their applications in iterative methods, convex and pseudo-convex minimization(proximal point algorithm), fixed point theory and equilibrium problems. The results extend several new results in the literature and some of them seem new even in Hilbert spaces.