IJPAM: Volume 113, No. 5 (2017)

Title

FIXED POINT THEOREMS FOR GENERALIZED
$(\alpha$-$\psi)$-CONTRACTIVE MAPPINGS
IN MULTIPLICATIVE METRIC SPACES

Authors

Parveen Kumar$^1$, Shin Min Kang$^2$, Sanjay Kumar$^3$,
Chahn Yong Jung$^4$
$^{1,3}$Departement of Mathematics
Deenbandhu Chhotu Ram University
of Science and Technology
Murthal, Sonepat, 131039, Haryana, INDIA
$^2$Department of Mathematics and RINS
Gyeongsang National University
Jinju, 52828, KOREA
$^4$Department of Business Administration
Gyeongsang National University
Jinju 52828, KOREA

Abstract

In this paper, we discuss generalized $(\alpha$-$\psi)$-contractive mappings in setting of multiplicative metric spaces and obtain the existence and the uniqueness of fixed points for these mappings.

History

Received: November 30, 2016
Revised: February 1, 2017
Published: April 1, 2017

AMS Classification, Key Words

AMS Subject Classification: 47H10, 54H25
Key Words and Phrases: multiplicative metric spaces, generalized $(\alpha$-$\psi)$-contractive mappings, $\alpha$-admissible mappings, fixed points

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Bibliography

1
H.H. Alsulami, S. Chandok, M.A. Taoudi, I.M. Erhan, Some fixed point theorems for $(\alpha,\psi)$-rational type contractive mappings, Fixed Point Theory Appl., 97 (2015) 12 pages, doi: https://doi.org/10.1186/s13663-015-0332-3

2
A.E. Bashirov, E.M. Kurplnara, A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008) 36-48. doi: https://doi.org/10.1016/j.jmaa.2007.03.081

3
M. Özavsar, A.C. Çevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, arXiv: 1205.5131v1 [math.GM], 2012, 14 pages.

4
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for $\alpha$-$\psi$-contractive type mappings, Nonlinear Anal., 75 (2012) 2154-2165, doi: https://doi.org/10.1016/jj.na.2011.10.014

How to Cite?

DOI: 10.12732/ijpam.v113i5.7 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: 113
Issue: 5
Pages: 595 - 607


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