A Survey on Best Proximity Point Theory in Reflexive and Busemann Convex Spaces

Moosa Gabeleh ()
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Moosa Gabeleh: Ayatollah Boroujerdi University, Department of Mathematics

Chapter Chapter 9 in Advances in Metric Fixed Point Theory and Applications, 2021, pp 183-216 from Springer

Abstract: Abstract In this chapter, we present some best proximity point theorems for Kannan cyclic mappings in the setting of Busemann convex spaces which are reflexive. To this end, we recall some results obtained in the framework of the fixed point theory for Kannan self mappings and generalize them to cyclic mappings in order to study the existence of best proximity points. We do it from two different approaches. The first one is based on a geometric property defined on a nonempty and convex pair in a geodesic space, called proximal normal structure, and the other one will be done by considering some sufficient conditions on the cyclic mappings. We also study the structure of minimal sets for Kannan cyclic nonexpansive mappings.

Keywords: Best proximity point; Kannan cyclic mapping; Busemann convex space; Proximal quasi-normal structure (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-6647-3_9

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DOI: 10.1007/978-981-33-6647-3_9

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