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

In: Advances in Metric Fixed Point Theory and Applications

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  • Moosa Gabeleh

    (Ayatollah Boroujerdi University, Department of Mathematics)

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.

Suggested Citation

  • Moosa Gabeleh, 2021. "A Survey on Best Proximity Point Theory in Reflexive and Busemann Convex Spaces," Springer Books, in: Yeol Je Cho & Mohamed Jleli & Mohammad Mursaleen & Bessem Samet & Calogero Vetro (ed.), Advances in Metric Fixed Point Theory and Applications, chapter 0, pages 183-216, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_9
    DOI: 10.1007/978-981-33-6647-3_9
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