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A new concept of set-valued Mizoguchi-Takahashi G-contractions is introduced in this paper and some fixed point theorems for such mappings in b-metric spaces endowed with directed graphs are established under some suffcient conditions. Our results improve and extend those of [20] and [24]. We also give some examples supporting our main results. As an applications, we prove the existence of fixed points for multivalued mappings satisfying generalized MT-contractive condition in ϵ-chainable b-metric spaces and the existence of a solution for some integral equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new class of generalized Berinde-type (&#951,ξ,ν,θ)-contractive in b-metric space and establish some fixed and common fixed point results for the class of mappings in partially ordered complete b-metric spaces. Our results generalize and extend several known results from the context of ordered metric spaces to the setting of ordered b-metric spaces. [ABSTRACT FROM AUTHOR]