A COMMON FIXED POINT THEOREM FOR WEAKLY COMPATIBLE MAPPINGS

By

N. Chandra¹ , Bharti Joshi² , M. C. Arya³ and Mahesh C. Joshi⁴

¹Department of Mathematics, S. N. S. Government Postgraduate College, Narayan Nagar, Pithoragarh-262550, Uttarakhand, India

^2,4 Department of Mathematics, D. S. B. Campus, Kumaun University, Nainital-263002, Uttarakhand, India

³Department of Mathematics, B. S. R. Government Degree College, Rikhanikhal, Pauri-246179 Garhwal, Uttarakhand, India Email:cnaveen329@gmail.com, bhartijoshi20592@gmail.com, mcarya1986@gmail.com, mcjoshi69@gmail.com

(Received : October 29, 2021; Revised : November 15, 2021; In final form : December 30, 2021)

DOI: https://doi.org/10.58250/Jnanabha.2021.51234

Abstract

The aim of the paper is to obtain a common fixed point theorem for a (ψ, φ)-weak contraction under a generalized rational type condition in a complete metric space. Our result generalizes many well known theorems of literature.

2020 Mathematical Sciences Classification: 47H10, 54H25.

Keywords and Phrases: Weak compatibility, (ψ, φ)-weak contraction, common fixed point.

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