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May 2018 On generalized pointwise noncyclic contractions without proximal normal structure
Moosa Gabeleh
Ann. Funct. Anal. 9(2): 220-232 (May 2018). DOI: 10.1215/20088752-2017-0049

Abstract

In this article, we introduce a new class of noncyclic mappings called generalized pointwise noncyclic contractions, and we prove a best proximity pair theorem for this class of noncyclic mappings in the setting of strictly convex Banach spaces. Our conclusions generalize a result due to Kirk and Royalty. We also study convergence of iterates of noncyclic contraction mappings in uniformly convex Banach spaces.

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Moosa Gabeleh. "On generalized pointwise noncyclic contractions without proximal normal structure." Ann. Funct. Anal. 9 (2) 220 - 232, May 2018. https://doi.org/10.1215/20088752-2017-0049

Information

Received: 22 December 2016; Accepted: 16 May 2017; Published: May 2018
First available in Project Euclid: 7 December 2017

zbMATH: 06873699
MathSciNet: MR3795087
Digital Object Identifier: 10.1215/20088752-2017-0049

Subjects:
Primary: 46B20 , 47H09 , 47H10

Keywords: best proximity pair , generalized pointwise noncyclic contraction , iterate sequence , strictly convex Banach space

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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