Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map
Articles
Prabavathy Magadevan
Bharathidasan University
https://orcid.org/0000-0003-2722-6395
Saravanan Karpagam
Saveetha Institute of Medical and Technical Sciences
Erdal Karapınar
China Medical University
https://orcid.org/0000-0002-6798-3254
Published 2022-01-01
https://doi.org/10.15388/namc.2022.27.25188
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Keywords

p-cyclic map
fixed point
best proximity point
p-cyclic orbital nonexpansive map

How to Cite

Magadevan P., Karpagam S. and Karapınar E. (2022) “Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map”, Nonlinear Analysis: Modelling and Control, 27(1), pp. 91-101. doi: 10.15388/namc.2022.27.25188.

Abstract

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

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