Displaying similar documents to “Linear openness of multifunctions in metric spaces.”

Spaces of ω-limit sets of graph maps

Jie-Hua Mai, Song Shao (2007)

Fundamenta Mathematicae

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Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.

Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

Mehmet Kir, Esra Yolacan, Hukmi Kiziltunc (2017)

Open Mathematics

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The purpose of this paper is to present some existence results for coupled fixed point of a (φ,ψ) -contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the results.