Common fixed points of \(\alpha\)-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space

Volume 10, Issue 7, pp 3456--3476 http://dx.doi.org/10.22436/jnsa.010.07.10

Publication Date: July 22, 2017 Submission Date: August 31, 2016

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Authors

Abdulaziz Saleem Moslem Alofi - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Abdullah Eqal Al-Mazrooei - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia. Bahru Tsegaye Leyew - Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa. Mujahid Abbas - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, University of Management and Technology, C-II Johar Town, Lahore, Pakistan.

Abstract

In this paper, we introduce the concept of \(\alpha\)-dominated multivalued mappings and establish the existence of common fixed points of such mappings on a closed ball contained in left/right K-sequentially complete dislocated quasi b-metric spaces. These results improve, generalize, extend, unify, and complement various comparable results in the existing literature. Our results not only extend some primary results to left/right K-sequentially dislocated quasi b-metric spaces but also restrict the contractive conditions on a closed ball only. Some examples are presented to support the results proved herein. Finally as an application, we obtain some common fixed point results for single-valued mappings by an application of the corresponding results for multivalued mappings satisfying the contractive conditions more general than Banach type and Kannan type contractive conditions on closed balls in a left K-sequentially complete dislocated quasi b-metric space endowed with an arbitrary binary relation.

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Keywords

• K-sequentially complete
• dislocated quasi b-metric spaces
• \(\alpha\)-dominated multivalued mapping
• closed ball
• common fixed point.

MSC

•  47H04
•  47H07
•  47H10

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