On quasi-contractions in metric spaces with a graph

Year 2016, Volume: 45 Issue: 4, 1033 - 1047, 01.08.2016

Kamal Fallahi Aris Aghanians

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

References

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