Best Proximity Points of MT-Cyclic Contractions with Property UC

Abstract

We initiate the notion of generalized $\mathcal{M}\mathcal{T}$- cyclic contraction mappings with respect to an auxiliary function $\phi$ and investigate the existence of a best proximity point of such mappings in the setting of metric spaces. We also prove the uniqueness of a fixed point, when we assume an additional condition, named as: property UC. Moreover, we discuss the existence and uniqueness of a fixed point of $\mathcal{M}\mathcal{T}$-cyclic orbital contractions in the context of (b-metric) metric spaces.

Keywords:

• Best proximity point
• cyclic map
• $\mathcal{M}\mathcal{T}$-cyclic orbital contraction
• property UC

1991 MATHEMATICS SUBJECT CLASSIFICATION:

• 46T99
• 47T10
• 54H25

Acknowledgment

The second author wish to express their hearty thanks to Professor Erdal Karap inar for valuable suggestions for this paper.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work has been financially supported by the Payame Noor University (PNU), I.R. of Iran under the first author grant (Hossein Lakzian).