Some fixed point theorems concerning (\(\psi,\phi\))-type contraction in complete metric spaces

Volume 9, Issue 6, pp 4127--4136 http://dx.doi.org/10.22436/jnsa.009.06.56

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Authors

Xin-Dong Liu - Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. Shih-Sen Chang - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Yun Xiao - Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. Liang-Cai Zhao - Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China.

Abstract

The purpose of this paper is to introduce the notions of (\(\psi,\phi\))-type contractions and (\(\psi,\phi\))-type Suzuki contractions and to establish some new fixed point theorems for such kind of mappings in the setting of complete metric spaces. The results presented in the paper are an extension of the Banach contraction principle, Suzuki contraction theorem, Jleli and Samet fixed point theorem, Piri and Kumam fixed point theorem.

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Keywords

• Contraction principle
• fixed point
• (\(\psi،\phi\))-type contraction
• ( \(\psi،\phi\))-type Suzuki contraction.

MSC

•  47J25
•  47H09
•  65K10

References

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