#### Mujahid Abbas, Ismat Beg, Bahru Tsegaye Leyew, Common fixed points of $(R,\alpha )$-generalized rational multivalued contractions in R-complete b-metric spaces, Vol. 2019 (2019), Article ID 14, pp. 1-17

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DOI: 10.23952/cot.2019.14

Received May 30, 2019; Accepted July 23, 2019; Published August 21, 2019

Abstract. In this paper, we introduce the concept of the $R$-continuity and the $R$-closedness for a pair of multivalued mappings. A new class of $(R,\alpha )$-generalized rational multivalued contraction mappings is defined. We establish the existence of common fixed points of such mappings in the framework of $b$-metric spaces endowed with an arbitrary binary relation $R$. Existence of fixed and common fixed points of single valued mappings is shown in the setting of $R$-complete $b$-metric spaces. Several examples are constructed in support of our new results.

Mujahid Abbas, Ismat Beg, Bahru Tsegaye Leyew, Common fixed points of $(R,\alpha )$-generalized rational multivalued contractions in $R$-complete $b$-metric spaces, Communications in Optimization Theory, Vol. 2019 (2019), Article ID 14, pp. 1-17.