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

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DOI:

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

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.

 

Keywords

t-norm , compatible mappings , reciprocal continuity , subcompatible mappings , subsequential continuity
  • 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.
  • Pages: 31-44
  • Date Published: 2013-10-01
  • Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal

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Published

2013-10-01

How to Cite

[1]
S. Chauhan, B. D. Pant, and M. Imdad, “Coincidence and common fixed point theorems in Non-Archimedean Menger PM-spaces”, CUBO, vol. 15, no. 3, pp. 31–44, Oct. 2013.

Issue

Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal

Section

Articles