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Fixed point results for Hardy-Rogers type contractions with respect to a \(c\)-distance in graphical cone metric spaces. (English) Zbl 07268335

Summary: The aim of this paper is to prove some existence and uniqueness results of the fixed points for Hardy-Rogers type contraction in cone metric spaces associated with a \(c\)-distance and endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally \(G\)-continuity of mapping instead of the condition of continuity, and consider cone metric spaces endowed with a graph instead of cone metric spaces.

MSC:

47H10 Fixed-point theorems
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
05C20 Directed graphs (digraphs), tournaments
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References:

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