A generalized \(\theta\)-contraction and related fixed point theorems

Volume 10, Issue 9, pp 4724--4733 http://dx.doi.org/10.22436/jnsa.010.09.15

Publication Date: September 09, 2017 Submission Date: May 24, 2016

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Authors

Mohamed Jleli - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia. Bessem Samet - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract

We introduce two types of generalized \(\theta\)-contraction mappings in complete metric spaces. For each type, we study the existence of fixed points. The obtained results in this paper generalize several existing fixed point theorems in the literature. We end this work with some open questions.

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Keywords

• Fixed point
• generalized \(\theta\)-contraction of type (I)
• generalized \(\theta\)-contraction of type (II)
• partial order
• \(\theta\)-cyclic contraction.

MSC

•  47H10

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