Author:
Sintunavarat Wutiphol,Cho Yeol Je,Kumam Poom
Abstract
Abstract
Recently, the complex-valued metric spaces which are more general than the metric spaces were first introduced by Azam et al. (Numer. Funct. Anal. Optim. 32:243-253, 2011). They also established the existence of fixed point theorems under the contraction condition in these spaces. The aim of this paper is to introduce the concepts of a C-Cauchy sequence and C-complete in complex-valued metric spaces and establish the existence of common fixed point theorems in C-complete complex-valued metric spaces. Furthermore, we apply our result to obtain the existence theorem for a common solution of the Urysohn integral equations
x
(
t
)
=
∫
a
b
K
1
(
t
,
s
,
x
(
s
)
)
d
s
+
g
(
t
)
,
x
(
t
)
=
∫
a
b
K
2
(
t
,
s
,
x
(
s
)
)
d
s
+
h
(
t
)
,
where
t
∈
[
a
,
b
]
⊆
R
,
x
,
g
,
h
∈
C
(
[
a
,
b
]
,
R
n
)
and
K
1
,
K
2
:
[
a
,
b
]
×
[
a
,
b
]
×
R
n
→
R
n
.
MSC:47H09, 47H10.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference26 articles.
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5. Mustafa Z, Sims B: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 2006, 7: 289-297.
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