Abstract and Applied Analysis

Fixed Point Theory in $\alpha$-Complete Metric Spaces with Applications

Abstract

The aim of this paper is to introduce new concepts of $\alpha$-$\eta$-complete metric space and $\alpha$-$\eta$-continuous function and establish fixed point results for modified $\alpha$-$\eta$-$\psi$-rational contraction mappings in $\alpha$-$\eta$-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for $\psi$-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 280817, 11 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607387

Digital Object Identifier
doi:10.1155/2014/280817

Mathematical Reviews number (MathSciNet)
MR3166589

Zentralblatt MATH identifier
07022081

Citation

Hussain, N.; Kutbi, M. A.; Salimi, P. Fixed Point Theory in $\alpha$ -Complete Metric Spaces with Applications. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 280817, 11 pages. doi:10.1155/2014/280817. https://projecteuclid.org/euclid.aaa/1412607387

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