Annals of Functional Analysis

On generalized pointwise noncyclic contractions without proximal normal structure

Moosa Gabeleh

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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.

Article information

Ann. Funct. Anal. Volume 9, Number 2 (2018), 220-232.

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

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Digital Object Identifier

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 46B20: Geometry and structure of normed linear spaces

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


Gabeleh, Moosa. On generalized pointwise noncyclic contractions without proximal normal structure. Ann. Funct. Anal. 9 (2018), no. 2, 220--232. doi:10.1215/20088752-2017-0049.

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