An extension of trapezoid inequality to the complex integral
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Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Universitesi
Abstract
In this paper we extend the trapezoid inequality to the complex integral by providing upper bounds for the quantity
|
(
v
−
u
)
f
(
u
)
+
(
w
−
v
)
f
(
w
)
−
∫
γ
f
(
z
)
d
z
|
under the assumptions that
γ
is a smooth path parametrized by
z
(
t
)
,
t
∈
[
a
,
b
]
,
u
=
z
(
a
)
,
v
=
z
(
x
)
with
x
∈
(
a
,
b
)
and
w
=
z
(
b
)
while
f
is holomorphic in
G
, an open domain and
γ
∈
G
. An application for circular paths is also given.