# Fixed point theorems for ($\alpha,\eta,\psi,\xi$)-contractive multi-valued mappings on $\alpha-\eta$-complete partial metric spaces

Volume 9, Issue 5, pp 1977--1990 Publication Date: May 20, 2016
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### Authors

Ali Farajzadeh - Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149, Iran. 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.

### Abstract

In this paper, the notion of strictly ($\alpha,\eta,\psi,\xi$)-contractive multi-valued mappings is introduced where the continuity of $\xi$ is relaxed. The existence of fixed point theorems for such mappings in the setting of $\alpha,\eta$-complete partial metric spaces are provided. The results of the paper can be viewed as the extension of the recent results obtained in the literature. Furthermore, we assure the fixed point theorems in partial complete metric spaces endowed with an arbitrary binary relation and with a graph using our obtained results.

### Keywords

• $\alpha،\eta$-complete partial metric spaces
• $\alpha،\eta$-continuity
• ($\alpha،\eta،\psi،\xi$)-contractive multi-valued mappings
• $\alpha$-admissible multi-valued mappings with respect to $\eta$.

•  47H10
•  54H25

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