Some fixed point theorems for $\theta$-$\phi$ ${C}$-contractions

Volume 10, Issue 11, pp 5723--5733 Publication Date: November 15, 2017       Article History
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Authors

Dingwei Zheng - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China. Xinhe Liu - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China. Gengrong Zhang - College of Mathematics and Computationl Science, Hunan First Normal University, Changsha, Hunan, 410205, P. R. China.

Abstract

In this paper, we introduce the notion of $\theta$-$\phi$ ${C}$-contraction and establish some fixed point and coupled fixed point theorems for these mappings in the setting of complete metric spaces and ordered metric spaces. The results presented in the paper improve and extend some well-known results. Also, we give an example to illustrate them.

Keywords

• Fixed point
• coupled fixed point
• complete metric space
• $\theta$-$\phi$ ${C}$-contraction

•  47H10
•  54H25

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