Fixed point theorems for generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings in \(\alpha-\eta-\)complete metric spaces

Volume 9, Issue 2, pp 471--485 http://dx.doi.org/10.22436/jnsa.009.02.13

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Authors

Preeyaluk Chuadchawna - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. Anchalee Kaewcharoen - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. Somyot Plubtieng - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.

Abstract

In this paper, we introduce the concept of generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings and prove the unique fixed point theorems for such mappings in \(\alpha-\eta-\)complete metric spaces without assuming the subadditivity of \(\psi\). We also give an example for supporting the result and present an application using our main result to obtain a solution of the integral equation.

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Keywords

• \(\alpha-\eta-\)complete metric spaces
• \(\alpha-\eta-\)continuous mappings
• triangular \(\alpha-\)-orbital admissible mappings
• generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings.

MSC

•  47H10
•  54H25

References

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