Weak condition for generalized f-weakly Picard mappings on partial metric spaces

Volume 10, Issue 5, pp 2501--2509 http://dx.doi.org/10.22436/jnsa.010.05.19

Publication Date: May 25, 2017 Submission Date: December 21, 2016

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Authors

Xinchen Du - Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, P. R. China. Xianjiu Huang - Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, P. R. China. Chunfang Chen - Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, P. R. China.

Abstract

Recently, Minak and Altun introduced the notions of multivalued weak contractions and multivalued weakly Picard operators on partial metric spaces. They also obtained two fixed point theorems with the notions of multivalued (\(\delta\), L)– weak contractions and multivalued (\(\alpha\), L)-weak contractions. In this paper, we introduce the notion of generalized multivalued (f, \(\alpha, \beta\))-weak contraction on partial metric spaces. We also establish some coincidence and common fixed point theorems. Our results extend and generalize some well-known common fixed point theorems on partial metric spaces.

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Keywords

• Partial metric
• common fixed point
• hybrid maps
• weakly Picard operators.

MSC

•  47H10
•  54H25

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