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2017 A weak convergence theorem for mean nonexpansive mappings
Torrey M. Gallagher
Rocky Mountain J. Math. 47(7): 2167-2178 (2017). DOI: 10.1216/RMJ-2017-47-7-2167

Abstract

In this paper, we first prove that the iterates of a mean nonexpansive map defined on a weakly compact, convex set converge weakly to a fixed point in the presence of Opial's property and asymptotic regularity at a point. Next, we prove the analogous result for closed, convex (not necessarily bounded) subsets of uniformly convex Opial spaces. These results generalize the classical theorems for nonexpansive maps of Browder and Petryshyn in Hilbert space and Opial in reflexive spaces, satisfying Opial's condition.

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Torrey M. Gallagher. "A weak convergence theorem for mean nonexpansive mappings." Rocky Mountain J. Math. 47 (7) 2167 - 2178, 2017. https://doi.org/10.1216/RMJ-2017-47-7-2167

Information

Published: 2017
First available in Project Euclid: 24 December 2017

zbMATH: 06828635
MathSciNet: MR3743709
Digital Object Identifier: 10.1216/RMJ-2017-47-7-2167

Subjects:
Primary: 47H10

Keywords: asymptotically regular , mean nonexpansive , Opial's property , weak convergence

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 7 • 2017
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