On the Iterations of a Sequence of Strongly Quasi-Nonexpansive Mappings with Applications
Hadi Khatibzadeh, Vahid Mohebbi · Numerical Functional Analysis and Optimization · 2019
In this article, we study Δ-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 to 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. One of our motivations is to unify some usual iterative methods in fixed point theory and proximal methods using the iterations generated by a sequence of strongly nonexpansive mappings.