Yakov I. Alber, Differential inequalities and dynamical systems for fixed point problems, Vol. 2024 (2024), Article ID 24, pp. 1-33

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DOI: 10.23952/cot.2024.24

Received June 21, 2023; Accepted Septemer 18, 2023; Published online March 30, 2024

Abstract. In [18] and [19], we have recently studied a behavior of the iterative processes to find fixed points of nonexpansive self-mappings $S:\Omega \to \Omega$ using both total asymptotically nonexpansive approximations $S_k:\Omega \to \Omega$ and total asymptotically weakly contractive approximations $S_k,$ where $\Omega$ is a closed and convex set in a uniformly convex Banach space $B.$ We proved there strong and weak convergence of the corresponding iterative consequences. In the present paper we investigate the dynamical systems (1.14) with so called total asymptotically weakly contractive approximating family of operators $S(t): \Omega \to \Omega$ depending on continuous parameter $t \ge t_0 \ge 0.$ Part of the results deals with nonexpansive approximating family of operators $S(t).$ All our proofs are based on the estimates of solutions of the differential inequalities to which most of the paper is devoted.

How to Cite this Article:
Y. I. Alber, Differential inequalities and dynamical systems for fixed point problems, Commun. Optim. Theory 2024 (2024) 24.