Fixed point results for Pata contraction on a metric space with a graph and its application

Authors : Maryam RAMEZANİ, Asma ARİAN

Pages : 1831-1840

Doi:10.31801/cfsuasmas.467481

View : 11 | Download : 8

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :Let $insert ignore into journalissuearticles values(X,d);$ be a metric space endowed with a graph $G$ such that the set $Vinsert ignore into journalissuearticles values(G);$ 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