IJPAM: Volume 116, No. 2 (2017)

Title

COMMON FIXED POINT RESULTS FOR RATIONAL TYPE
CONTRACTION IN COMPLEX VALUED b-METRIC SPACES

Authors

A.K. Dubey$^1$, Manjula Tripathi$^2$, M.D. Pandey$^3$
$^{1,3}$Department of Mathematics
Bhilai Institute of Technology
Bhilai House, Durg, Chhattisgarh 491001, INDIA
$^2$Department of Mathematics
U.P.U. Govt. Polytechnic
Durg, Chhattisgarh 491001, INDIA

Abstract

In this paper, we present some results of fixed point theory in a recently introduced generalization of the metric space, that is, complex valued b-metric space where the metric assumes values in the set of complex number. The presented theorems extend and generalize the well known results in the literature.

History

Received: 2017-05-09
Revised: 2017-07-22
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 47H09, 47H10
Key Words and Phrases: common fixed point, complete complex valued b-metric space, Cauchy sequence

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Bibliography

1
A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and Optimization, Vol.32, No.3 (2011), pp 243-253.

2
A.K. Dubey, Common fixed point results for contractive mappings in complex valued b-metric spaces, Nonlinear Fuctional Analysis and Applications, Vol.20, No.2(2015), pp 257-268.

3
A.K. Dubey, Complex Valued b-Metric Spaces and Common Fixed Point Theorems under Rational Contractions, Journal of Complex Analysis, Vol. 2016, Article ID 9786063(2016), 7 Pages.

4
A.K. Dubey and Manjula Tripathi, Some generalized common fixed point theorems under rational contractions in Complex valued b-metric spaces and Applications, Asian Journal of Mathematics and Applications, Vol. 2016, Article ID ama0323(2016), 10 pages.

5
Anil Kumar Dubey and Manjula Tripathi, Common Fixed Point Theorem in Complex Valued b-Metric Space for Rational Contractions, Journal of Informatics and Mathematical Sciences, Vol.7, No.3(2015), pp.149-161.

6
Anil Kumar Dubey, Manjula Tripathi and Ravi Prakash Dubey, Various Fixed Point Theorems in Complex Valued b-Metric Spaces, International Journal of Engineering Mathematics, Vol. 2016, Article ID 7072606(2016), 7 Pages.

7
A.K. Dubey, Rita Shukla, Ravi Prakash Dubey, Some common fixed point theorems for contractive mappings in complex valued b-metric spaces, Asian Journal of Mathematics and Applications, Vol. 2015, Article ID ama0266, 13 Pages.

8
A.A. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces, The Scientific World Journal, Vol.2014(2014), Article ID 587825, 6 pages.

9
K. Sitthikul, S. Saejung, Some fixed point theorems in complex valued metric space, Fixed Point Theory Appl. (2012), 189.

10
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), pp 1-8.

11
Binayak S. Choudhury, Nikhilesh Metiya, Pulak Konar, Fixed Point Results for Rational type contraction in Partially ordered Complex Valued Metric Spaces, Bulletin of the International Mathematical Virtual Institute, Vol.5 (2015), pp 73-80.

12
W. Sintunavarat, P. Kumam, Generalized common fixed point theorems in Complex Valued metric spaces and applications, J. Inequal Appl. (2012), 84.

How to Cite?

DOI: 10.12732/ijpam.v116i2.16 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 447 - 456


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