On quasi-contractions in metric spaces with a graph

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Hacettepe Journal of Mathematics and Statistics
Volume:45 Issue:4
On quasi-contractions in metric spaces with a graph

On quasi-contractions in metric spaces with a graph

Authors : Kamal FALLAHİ, Aris AGHANİANS

Pages : 1033-1047

View : 49 | Download : 10

Publication Date : 2016-08-01

Article Type : Research Paper

Abstract :In the present work, we introduce G -quasi-contractions using directed graphs in metric spaces with a graph and we show that this contrac- tion generalizes a large number of contractions. the existence of xed points for We then investigate G -quasi-contractions under two dif- ferent conditions and discuss the main theorem. Finally, we list some consequences of our theorem where either the contractive condition is replaced with a stronger one or the underlying space is changed to a complete metric space or a complete cone metric space.
Keywords : G e Quasi contraction, Fixed point C, Graph

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