Fixed point results for Pata contraction on a metric space with a graph and its application
Let $(X,d)$ be a metric space endowed with a graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$. We define the notion of Pata-$G$-contraction type maps and obtain some fixed point theorems for such mappings. This extends and subsumes many recent results which were obtained for other contractive type mappings on a partially ordered metric space. As an application, we present theorem on the convergence of successive approximations for some linear operators on a Banach space.
Keywords:
Fixed point, Picard operator, Weakly connected graph, Pata-$G$-contraction Cauchy equivalent, Quasi-order,
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- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi
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