Fixed point results for generalized \((\alpha-\eta)-\Theta\) contractions with applications

Volume 10, Issue 8, pp 4197--4208 http://dx.doi.org/10.22436/jnsa.010.08.15

Publication Date: August 13, 2017 Submission Date: March 11, 2017

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Abdullah Eqal Al-Mazrooei - Department of Mathematics, University of Jeddah, P .O. Box 80327, Jeddah 21589, Saudi Arabia. Jamshaid Ahmad - Department of Mathematics, University of Jeddah, P .O. Box 80327, Jeddah 21589, Saudi Arabia.

Abstract

The aim of this paper is to define generalized \((\alpha-\eta)-\Theta\) contraction and to extend the results of Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., \(\bf{2014}\) (2014), 8 pages] by applying a simple condition on the function \(\Theta\). We also deduce certain fixed and periodic point results for orbitally continuous generalized \(\Theta \)-contractions and certain fixed point results for integral inequalities are derived. Finally, we provide an example to show the significance of the investigation of this paper.

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Keywords

• Fixed point
• complete metric space
• \(\alpha\)-admissible mapping.

MSC

•  47H10
•  54H25

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