\(C\)-class functions and fixed point theorems for generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings in \(\alpha-\eta-\)complete metric spaces

Volume 9, Issue 6, pp 4177--4190 http://dx.doi.org/10.22436/jnsa.009.06.60

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Authors

Arslan Hojat Ansari - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, 31485-313, Iran. Anchalee Kaewcharoen - Research Center for Academic Excellence in Mathematics, Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand.

Abstract

In this paper, we introduce the concept of generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings where \(\psi\) is the altering distance function and \(\varphi\) is the ultra altering distance function. The unique fixed point theorems for such mappings in the setting of \(\alpha-\eta-\)-complete metric spaces are proven. We also assure the fixed point theorems in partially ordered metric spaces. Moreover, the solution of the integral equation is obtained using our main result.

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Keywords

• \(\alpha-\eta-\)complete metric spaces
• \(\alpha-\eta-\)continuous mappings
• triangular \(\alpha\)-orbital admissible mappings with respect to \(\eta\)
• C-class functions
• generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings.

MSC

•  47H10
•  54H25

References

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