Existence and Uniqueness of a Common Best Proximity Point on Fuzzy Metric Space

Abstract

In this paper, first we introduce the notion of proximally weakly compatible mappings and we extend the CLRg property (CLRg-Common limit in the range of g) to the case of non-self mappings. Then we prove the existence of proximally coincident point for this new class of mappings with the assumption of proximal CLRg property in fuzzy metric space. Further, we establish new common best proximity point result for proximally weakly compatible mappings in the setting of fuzzy metric space.

KEYWORDS:

• Best proximity points
• fixed points
• weakly compatible mappings
• fuzzy metric space

Acknowledgments

The authors would like to thank the National Board for Higher Mathematics (NBHM), DAE, Govt. of India for providing a financial support under the grant number 02011/22/2017/R&D II/14080.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Board for Higher Mathematics: [grant number 02011/22/2017/R&D II/14080].

Notes on contributors

V. Pragadeeswarar

V. Pragadeeswarar was born in 1986 in Tamil Nadu, India. He received Master, MPhil and PhD degrees in Mathematics from Bharathidasan University, Trichy in 2009, 2010 and 2015, respectively. Currently, he is an Assistant Professor (Sr. G) in the Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India. He has published 10 research papers in international journals.

R. Gopi

R. Gopi received Master and MPhil degrees in Mathematics from Bharathidasan University, Trichy in 2011 and 2012, respectively. Now, he is a PhD student in Department of Mathematics, Amrita Vishwa Vidyapeetham, Coimbatore, India.