Common Fixed Point Theorem in Complex Valued $b$-Metric Space for Rational Contractions

Authors

  • Anil Kumar Dubey Department of Mathematics, Bhilai Institute Of Technology, Bhilai House, Durg, Chhattisgarh 490001
  • Manjula Tripathi Department of Mathematics, U.P.U. Govt. Polytechnic, Durg, Chattisgarh 491001

DOI:

https://doi.org/10.26713/jims.v7i3.305

Keywords:

Rational expressions, Complex valued $b$-metric space, Common fixed point

Abstract

In this paper we prove the common xed point theorem in complex valued b-metric space for rational contractions. Our results extend, generalize and improve the corresponding result of Uthayakumar and Prabakar [12].

Downloads

Download data is not yet available.

References

A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and Optimization, Vol.32, no.3 PP.243-253, 2011.

AA. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces, The Scientific World Journal, Vol.2014(2014), Article ID 587825, 6 pages, http://dx.doi.org/10.1155/2014/587825.

B. Fisher, M.S. Khan, Fixed points, common fixed points and constant mappings, Studia Sci. Math. Hungar.11 (1978) 467-470.

B.K. Dass, S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math. 6(1975), 1455-1458.

D.S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), 223-230.

F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computers and Mathematics with Applications, Vol.64, no. 6, 1866-1874, 2012.

I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal. 30 (1989), 26-37.

J. Roshan, V. Parvanch, S. Sedghi, N. Shobkolaci, W. Shatanawi, Common fixed points of almost generalized $(psi,phi)_s$-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Applications, (2013), 2013:159.

K.P.R. Rao, P.R Swamy, J.R. Prasad, A common fixed point theorem in complex valued b-metric spaces, Bulletin of Mathematics and Statistics Research, Vol. 1, Issue 1, 2013.

M. Ozturkon, M. Basarr, Some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra, Hacettepe Journal of Mathematics and statistics, 41(2)(2012), 211-222.

M. Arshad, E. Karapinar, J. Ahmad, Some Unique Fixed Point Theorems for Rational Contractions in Partially ordered Metric Spaces, Journal of Inequalities and Applications 2013, 2013:248, doi:10.1186/1029-242X-2013-248.

R. Uthayakumar and G.A. Prabakar, Common fixed point theorem in cone metric space for rational contractions, International Journal of Analysis and Applications, Vol.3, No.2 (2013), 112-118.

S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae 3(1922), 133-181.

S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena.46(1998) 263-276.

S. Datta, S. Ali, A common fixed point theorem under contractive condition in complex valued metric spaces, International Journal of Advanced Scientific and Technical Research, 6 (2) (2012), 467-475.

S. Bhatt, S. Chaukiyal, R.Dimri, Common fixed point of mappings satisfying rational inequality in complex valued metric spaces, International Journal of Pure and Applied Mathematics, 73 (2) (2011), 159-164.

W. Sintunavarat,P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications, (2012) 2012:84.

W. Sintunavarat, Y.J. Cho, P. Kumam, Urysohn integral equations approach by common fixed point in complex valued metric spaces, Adv. Differ. Equ. 2013,49(2013).

Downloads

Published

2015-12-31
CITATION

How to Cite

Dubey, A. K., & Tripathi, M. (2015). Common Fixed Point Theorem in Complex Valued $b$-Metric Space for Rational Contractions. Journal of Informatics and Mathematical Sciences, 7(3), 149–161. https://doi.org/10.26713/jims.v7i3.305

Issue

Vol. 7 No. 3 (2015)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.