Coincidence and common fixed point theorems in Non-Archimedean Menger PM-spaces

Sunny Chauhan; B. D. Pant; Mohammad Imdad

doi:10.4067/S0719-06462013000300004

Authors

Sunny Chauhan R.H. Government Postgraduate College, Kashipur-244713, (U.S. Nagar), Uttarakhand, India.
B. D. Pant Government Degree College, Champawat-262523, Uttarakhand, India.
Mohammad Imdad Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India.

DOI:

https://doi.org/10.4067/S0719-06462013000300004

Keywords:

t-norm, compatible mappings, reciprocal continuity, subcompatible mappings, subsequential continuity

Abstract

The object of this work is to point out a fallacy in the proof of Theorem 1 contained in the recent paper of Khan et al. [Jordan J. Math. Stat. (JJMS) 5(2) (2012), 137-150] proved in Non-Archimedean Menger PM-space by using the notions of sub-compatibility and sub-sequential continuity. We show that the results of Khan et al. [Jordan J. Math. Stat. (JJMS) 5(2) (2012), 137-150] can be recovered in two ways. Further, we establish some illustrative examples to show the validity of the main results. Our results improve a multitude of relevant fixed point theorems of the existing literature.