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

TL;DR

This paper investigates the convergence properties of iterative sequences involving strongly quasi-nonexpansive mappings in Hadamard spaces, with applications to optimization, fixed point theory, and equilibrium problems.

Contribution

It extends existing convergence results to broader classes of mappings and spaces, including new insights even within Hilbert spaces.

Findings

Established $ riangle$-convergence of iterations in Hadamard spaces

Proved strong convergence of Halpern-type regularizations

Applied results to convex minimization and fixed point problems

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.