Fixed and best proximity points for Kannan cyclic contractions in modular function spaces

Ilchev, Atanas; Zlatanov, Boyan

doi:10.1007/s11784-017-0459-4

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Mathematical Preliminaries1

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2018

2024

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Cited by 13 publications

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“…Lemma 2.1 and Lemma 2.2 from [ 16 ] are generalized in the general case of a function modular space [ 25 ] as far as any uniformly convex Banach space is a function modular space generated by a function modular ρ that satisfies and has -property. Therefore, Lemma 2.1 and Lemma 2.2 from [ 16 ] are particular cases of the results from [ 22 ] and [ 32 ] enriching the knowledge on the geometry of function modular spaces.…”

Section: Mathematical Preliminariesmentioning

confidence: 97%

Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

Choudhury

Maity

Metiya³

et al. 2018

J Inequal Appl

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In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space. We discuss two examples.

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