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2 results on '"Digar, Abhik"'

1. A characterization of weak proximal normal structure and best proximity pairs.

Author

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

Abstract

The aim of this paper is to address an open problem given in [Kirk et al. in J Math Anal Appl 463:461–476, (2018)]. We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove the existence of a best proximity pair in the setting of reflexive Banach spaces. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Existence of Best Proximity Pairs and a Generalization of Carathéodory Theorem.

Author

Digar, Abhik and Kosuru, G. Sankara Raju

Subjects
INITIAL value problems, GENERALIZATION, BANACH spaces
Abstract

A new class of mappings, called relatively continuous, is introduced and incorporated to elicit best proximity pair theorems for a non-self-mapping in the setting of reflexive Banach space. As a consequence we obtain a generalization of Carathéodory extension theorem for an initial value problem with L1 functions on the right hand side. [ABSTRACT FROM AUTHOR]

Published
2020
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