Convexity and best approximation in Banach spaces

Chakraborty, Uday Shankar

doi:10.1007/s12215-021-00611-z

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Best Proximity Theory1

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2022

2023

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Cited by 2 publications

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“…In this case, the point ϑ is a best approximant for T . The credit of pioneering best approximation theory goes to Ky Fan (1969) (refer [6] and references therein for more details of best approximation theory). But the problem arises when A is mapped into another subset B of X by T .…”

Section: Best Proximity Theorymentioning

confidence: 99%

On a new variant of F-contractive mappings with application to fractional differential equations

Patlea

Gabeleh

2022

NAMC

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The present article intends to prove the existence of best proximity points (pairs) using the notion of measure of noncompactness. We introduce generalized classes of cyclic (noncyclic) F-contractive operators, and then derive best proximity point (pair) results in Banach (strictly convex Banach) spaces. This work includes some of the recent results as corollaries. We apply these conclusions to prove the existence of optimum solutions for a system of Hilfer fractionaldifferential equations.

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Section: Best Proximity Theorymentioning

confidence: 99%