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

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Alofi, Abdulaziz Saleem Moslem
Al-Mazrooei, Abdullah Eqal
Leyew, Bahru Tsegaye
Abbas, Mujahid

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International Scientific Research Publications (ISRP)

Abstract

In this paper, we introduce the concept of -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, -Dominated multivalued mapping, Closed ball, Common fixed point

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Citation

Alofi, A.S.M., Al-Mazrooei, A.E., Leyew, B.T. & Abbas, M. 2017, 'Common fixed points of alpha-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space', Journal of Nonlinear Sciences and Applications, vol. 10, pp. 3456-3476.