A characterization of weak proximal normal structure and best proximity pairs

Digar, Abhik; García, Rafael Espínola; Kosuru, G. Sankara Raju

doi:10.1007/s13398-022-01217-5

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2024

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Cited by 3 publications

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“…A similar notion requiring continuity was initially considered in [19] in relation to mappings with diminishing orbital diameters. More recently, orbit conditions have been considered in the study of existence of best proximity points for cyclic and noncyclic mappings [4,10,27].…”

Section: Mjommentioning

confidence: 99%

Fixed Points and Common Fixed Points for Orbit-Nonexpansive Mappings in Metric Spaces

2023

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In this paper, we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric spaces. The innovative concept studied here deals with nonexpansivity conditions with respect to orbits and under assumptions that only depend on the features of the closed balls of the metric space.

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