Common fixed point results of generalized almost rational contraction mappings with an application

Volume 9, Issue 5, pp 2273--2288 http://dx.doi.org/10.22436/jnsa.009.05.30

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia. Huseyin Isik - Department of Mathematics, Faculty of Science, Gazi University, 06500-Teknikokullar, Ankara, Turkey. - Department of Mathematics, Faculty of Science and Arts, Mus Alparslan University, Mus 49100, Turkey. Mujahid Abbas - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia. - Department of Mathematics and Applied Mathematics, University Pretoria, Lynnwood Road, Pretoria 0002, South Africa.

Abstract

In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of self mappings on a complete metric space. Several common fixed point results for such mappings are proved. Our results extend and unify various results in the existing literature. An example and application to obtain the existence of a common solution of the system of functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the presented results.

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Keywords

• Point of coincidence
• common fixed point
• cyclic admissible mappings
• almost contractions
• weakly compatible mappings
• functional equations.

MSC

•  47H10
•  54H25

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