IJPAM: Volume 109, No. 4 (2016)

A COUPLED FIXED POINT THEOREM IN $b$-METRIC SPACES

Wasfi Shatanawi$^1$, Mohammad Bani Hani$^2$
$^1$Department of Mathematics and General Courses
Prince Sultan University
Riyadh, SAUDI ARABIA
$^1$Department of Mathematics
Hashemite University
Zarqa, JORDAN
$^2$Department of Mathematics
Faculty of Science
Irbid National University
Irbid, JORDAN

Abstract. In this paper, we utilize the notion of coupled fixed point in sense of Bhaker and Lakshmikantham [T. Bhakar, V. Lakshmikantham, Fixed point theorems in partially orderd metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393] to introduce and prove a coupled fixed point theorem in a $b$-metric space. Our contractive condition is the most general contractive form in linear form. Our results modified and generalized many exciting results in the literature.

Received: August 3, 2016

Revised: September 3, 2016

Published: October 9, 2016

AMS Subject Classification: 47H10, 54H25

Key Words and Phrases: fixed point, common fixed point, $b$-metric space, quasi-contraction, metric spaces
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DOI: 10.12732/ijpam.v109i4.12 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: 2016
Volume: 109
Issue: 4
Pages: 889 - 897


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