Common fixed points of generalized rational contractions on a closed ball in partial metric spaces

Volume 10, Issue 10, pp 5261--5270 http://dx.doi.org/10.22436/jnsa.010.10.12

Publication Date: October 19, 2017 Submission Date: March 25, 2017

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Authors

Muhammad Nazam - Department of Mathematics, International Islamic University, Islamabad, Pakistan. Muhammad Arshad - Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan. Choonkil Park - Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea. Sungsik Yun - Department of Financial Mathematics, Hanshin University, Gyeonggi-do 18101, Republic of Korea.

Abstract

The notion of generalized contractions of rational type on a closed ball is introduced and used to establish some common fixed point theorems for two, three and four mappings in complete ordered partial metric spaces. These results improve several well-known, primary and conventional results. We give an example to illustrate the main idea of our results that there are mappings which have only fixed points inside or on the closed ball instead of whole space.

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Keywords

• Common fixed point
• closed ball
• generalized contraction
• partial metric space

MSC

•  47H09
•  47H10
•  54H25

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