Pythagorean Property and Asymptotic Relatively Nonexpansive Mappings

The aim of this article is to study the existence of best proximity pairs for asymptotic relatively nonexpansive mappings using a geometric notion of the Pythagorean property. In this way, we establish an existence theorem under some different conditions with respect to the same result of Rajesh and...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 15; no. 3; pp. 1 - 15
Main Authors Gabeleh, M., Markin, J.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2018
Springer Nature B.V
Subjects
Asymptotic properties
Existence theorems
Mathematics
Mathematics and Statistics
47H10
47H09
46B20
Best proximity pair
Pythagorean property
asymptotically relatively nonexpansive mapping
Busemann convex space
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Summary:The aim of this article is to study the existence of best proximity pairs for asymptotic relatively nonexpansive mappings using a geometric notion of the Pythagorean property. In this way, we establish an existence theorem under some different conditions with respect to the same result of Rajesh and Veeramani (Numer Funct Anal Optim 37:80–91, 2016 ). We also prove a best proximity point theorem for cyclic relatively nonexpansive mappings which are compact in the setting of reflexive Busemann convex spaces. An illustrative example will be presented to show the usability of our conclusions.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-018-1136-6