- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 2
- Fixed point results for Pata contraction on a metric space with a graph and its application
Fixed point results for Pata contraction on a metric space with a graph and its application
Authors : Maryam Ramezani, Asma Arian
Pages : 1831-1840
Doi:10.31801/cfsuasmas.467481
View : 10 | Download : 5
Publication Date : 2019-08-01
Article Type : Research
Abstract :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