Geodesic
Common fixed points of $\alpha$-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space
Alofi, Abdulaziz Saleem Moslem1 ; Al-Mazrooei, Abdullah Eqal2 ; Leyew, Bahru Tsegaye3 ; Abbas, Mujahid4
1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 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
3 Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa
4 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
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 7, p. 3456-3476.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.07.10
Classification : 47H04, 47H07, 47H10
Keywords: K-sequentially complete, dislocated quasi b-metric spaces, \(\alpha\)-dominated multivalued mapping, closed ball, common fixed point.

Alofi, Abdulaziz Saleem Moslem 1 ; Al-Mazrooei, Abdullah Eqal 2 ; Leyew, Bahru Tsegaye 3 ; Abbas, Mujahid 4

1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 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
3 Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa
4 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 
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Alofi, Abdulaziz Saleem Moslem; Al-Mazrooei, Abdullah Eqal; Leyew, Bahru Tsegaye; Abbas, Mujahid. Common fixed points of \(\alpha\)-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 7, p. 3456-3476. doi : 10.22436/jnsa.010.07.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.07.10/

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