In this paper we introduce the notion of (α * − ψ)-Ćirić-type contractive multivalued operator and investigate the existence and uniqueness of fixed point for such a mapping in b-metric spaces. The wellposedness of the fixed point problem and the Ulam-Hyres stability is also studied.

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The purpose of this paper is to present some existence results for coupled fixed points of contraction type operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Gnana Bhaskar and Lakshmikantham in (Nonlinear Anal. 65:1379-1393, 2006. As an application, the existence of a continuous solution for a system of Fredholm and Volterra integral equations is obtained. MSC: 47H10; 54H25Keywords: fixed point; coupled fixed point; metric space; connected graph PreliminariesIn fixed point theory, the importance of study of coupled fixed points is due to their applications to a wide variety of problems. Bhaskar and Lakshmikantham [] gave some existence results for coupled fixed point for a mixed monotone type mapping in a metric space endowed with partial order, using a weak contractivity type of assumption.The purpose of this paper is to generalize these results using the context of metric spaces endowed with a graph. This new research direction in the theory of fixed points was initiated by Jachymski Let (X, d) be a metric space and be the diagonal of X × X. Let G be a directed graph, such that the set V (G) of its vertices coincides with X and ⊆

In this manuscript, we introduce Meir-Keeler type contractions and Geraghty type contractions in the setting of the wt-distances over b-metric spaces. We examine the existence of a fixed point for such mappings. Under some additional assumption, we proved the uniqueness of the found fixed point.

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