Annals of Functional Analysis

On generalized pointwise noncyclic contractions without proximal normal structure

Moosa Gabeleh

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1512637231

Digital Object Identifier
doi:10.1215/20088752-2017-0049

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.afa/1512637231


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References

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