Fixed point results for multivalued mappings on a sequence in a closed ball with applications

Volume 17, Issue 2, pp 308-316 http://dx.doi.org/10.22436/jmcs.017.02.13

Publication Date: June 15, 2017 Submission Date: March 29, 2016

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Authors

Abdullah Shoaib - Department of Mathematics and Statistics, Riphah International University, Islamabad - 44000, Pakistan. Akbar Azam - Department of Mathematics, COMSATS Institute of Information Technology, Chack Shahzad, Islamabad - 44000, Pakistan. Muhammad Arshad - Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan. Eskandar Ameer - Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.

Abstract

In this paper, we establish fixed point results for semi \(\alpha_*\)-admissible multivalued mappings satisfying a contractive condition of Reich type only for the elements in a sequence contained in closed ball in a complete dislocated metric space. As an application, we derive some new fixed point theorems for ordered metric space and metric space endowed with a graph. An example has been constructed to demonstrate the novelty of our results. Our results unify, extend, and generalize several comparable results in the existing literature.

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Keywords

• Fixed point
• complete dislocated metric space
• closed ball
• \(\alpha_*\)- admissible.

MSC

•  46S40
•  47H10
•  54H25

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