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