Approximate fixed points of set-valued mapping in b-metric space

Volume 9, Issue 6, pp 3760--3772 http://dx.doi.org/10.22436/jnsa.009.06.26

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Authors

Bessem Samet - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, 11451 Riyadh, King Saudi Arabia. Calogero Vetro - Department of Mathematics and Computer Sciences, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy. Francesca Vetro - Department of Energy, Information Engineering and Mathematical Models (DEIM), University of Palermo, Viale delle Scienze, 90128, Palermo, Italy.

Abstract

We establish existence results related to approximate fixed point property of special types of set-valued contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some fixed point results which generalize and extend various fixed point theorems in the existing literature. A simple example illustrates the new theory. Finally, we apply our results to establishing the existence of solution for some differential and integral problems.

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Keywords

• b-metric space
• \(\eta\)-contraction
• fixed point theorem
• integral inclusion.

MSC

•  54H25
•  47H10
•  34A60

References

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