Weakly \(\mathbf{(s,r)}\)-contractive multi-valued operators on \(\mathbf{b}\)-metric space

Volume 11, Issue 3, pp 358--367 http://dx.doi.org/10.22436/jnsa.011.03.04

Publication Date: February 14, 2018 Submission Date: July 03, 2017 Revision Date: October 13, 2017 Accteptance Date: December 18, 2017

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Authors

Lingjuan Ye - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China. Congcong Shen - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China.

Abstract

In this paper we introduce the notion of weakly \((s,r)\)-contractive multi-valued operator on \(b\)-metric space and establish some fixed point theorems for this operator. In addition, an application to the differential equation is given to illustrate usability of obtained results.

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Keywords

• \(b\)-metric space
• weakly \((s
• r)\)-contractive multi-valued operator
• fixed point theorem

MSC

•  47H04
•  47H09
•  47H10

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