Communications in Mathematical Analysis

Convergence to Attractors of Nonexpansive Set-Valued Mappings

Simeon Reich and Alexander J. Zaslavski

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Abstract

In our previous work we have shown that if for any initial point there exists a trajectory of a nonexpansive set-valued mapping attracted by a given set, then this property is stable under small perturbations of the mapping. In the present paper we obtain several extensions of this result.

Article information

Source
Commun. Math. Anal., Volume 22, Number 1 (2019), 51-60.

Dates
First available in Project Euclid: 20 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.cma/1566266427

Mathematical Reviews number (MathSciNet)
MR3992901

Subjects
Primary: 47H04: Set-valued operators [See also 28B20, 54C60, 58C06] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54E35: Metric spaces, metrizability 54E50: Complete metric spaces

Keywords
attractor complete metric space iterative scheme nonexpansive set-valued mapping

Citation

Reich, Simeon; Zaslavski, Alexander J. Convergence to Attractors of Nonexpansive Set-Valued Mappings. Commun. Math. Anal. 22 (2019), no. 1, 51--60. https://projecteuclid.org/euclid.cma/1566266427


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