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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.29 No.4

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Best Proximity Point Theorems for Cyclic θ-­φ-­contraction on Metric Spaces

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2022, v.29 no.4, pp.335-352
https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.4.335
Rossafi, Mohamed
Kari, Abdelkarim
Lee, Jung Rye
Rossafi,, M. , Kari,, A. , & Lee,, J. R. (2022). Best Proximity Point Theorems for Cyclic θ-­φ-­contraction on Metric Spaces. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 29(4), 335-352, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.4.335

Abstract

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

keywords
fixed point, best proximity point, uniformly convex Banach space, <tex> ${\theta}$</tex>-contraction, <tex> ${\theta}-{\phi}$</tex>-contraction

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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