A note on coincidence points of multivalued weak G-contraction mappings

Volume 9, Issue 6, pp 4098--4103 http://dx.doi.org/10.22436/jnsa.009.06.53

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Authors

Monther Rashed Alfuraidan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. Mohamed Amine Khamsi - Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, U. S. A..

Abstract

In this note, we discuss the definition of the multivalued weak contraction mappings defined in a metric space endowed with a graph as introduced by Hanjing and Suantai[A. Hanjing, S. Suantai, Fixed Point Theory Appl., 2015 (2015), 10 pages]. In particular, we show that this definition is not correct and give the correct definition of the multivalued weak contraction mappings defined in a metric space endowed with a graph. Then we prove the existence of coincidence points for such mappings.

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Keywords

• Directed graph
• coincidence points
• weak G-contraction mappings
• Reich multivalued mapping.

MSC

•  47H09
•  46B20
•  47H10
•  47E10

References

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