Research Article

Rational contraction in multiplicative metric spaces

Volume: 2 Number: 4 December 24, 2018
EN

Rational contraction in multiplicative metric spaces

Abstract

The purpose of this paper is to prove that instead of a rational contraction shown in the papers  Afrah A. N. Abdou, \emph{Fixed point theorems for generalized contraction mappings in multiplicative metric spaces, }J. Nonlinear Sci.
Appl. 9, 2347-2363,  (2016) and N. Sharma, K. Kumar, S. Sharma, R. Jha, \emph{Rational contractive condition
in multiplicative metric space and common fixed point theorem}, International Journal of Innovative Research in Science,
Engineering and Technology, 5, 10473-10480 (2016) a more general contractive condition can be obtained in multiplicative metric spaces, which is equivalent to a contractive condition in metric spaces.

Keywords

References

  1. [1] M. Abbas, B. Ali, Yi Suleiman, \emph{Common fixed points oflocally contractive mappings in multiplicative metric spaces withapplications,} Int. J., Math. Math. Sci. 2015, Article ID 218683, (2015).
  2. [2] M. Abbas, M. De La Sen, T. Nazir, \emph{Common fixed pointsof generalized rational type cocyclic mappings in multiplicative metricspaces,} Discrete Dyn. Nat. Soc. 2015, Article Id 532725, (2015).
  3. [3] K. Abodayeh, A. Pitea, W. Shatanawi, T. Abdeljawad, \emph{%Remarks on Multiplicative Metric Spaces and Related Fixed Points,}arXiv:1512.03771v1 [math.GN] 11, (2015).
  4. [4] Afrah A. N. Abdou, \emph{Fixed point theorems for generalizedcontraction mappings in multiplicative metric spaces, }J. Nonlinear Sci.Appl. 9, 2347-2363, (2016).
  5. [5] D.E. Anderson, K.L.Singh, J.H.M. Whitfield, \emph{Common fixed point for family of mappings}, Internat. J. Math. and Math. Sci., 7(1), 1984, 89-95.
  6. [6] R. P. Agarwal, E. Karapinar and B. Samet, \emph{An essentialremark on fixed point results on multiplicative metric spaces, }Fixed Point\theory Appl., 2016:21, (2016).
  7. [7] S. Banach, \emph{Sur les op\'{e}rations dans les ensemblesabstraits et leur application aux \'{e}quations int\'{e}grales,} Fundam.Math.,3, 133-181, (1922).
  8. [8] A. Bashirov, E. Kurpinar, A. Ozyapici, \emph{Multiplicativecalculus and its applications,} J. Math. Anal. Appl. 337 (1), 36-48, (2008).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

December 24, 2018

Submission Date

November 13, 2018

Acceptance Date

December 7, 2018

Published in Issue

Year 2018 Volume: 2 Number: 4

Cited By