A New Generalization of Ostrowski's Integral Inequality for Mappings Whose Derivatives are
Bounded and Applications in Numerical Integration and for Special Means
This is the Published version of the following publication
Dragomir, Sever S, Cerone, Pietro and Roumeliotis, John (1999) A New Generalization of Ostrowski's Integral Inequality for Mappings Whose Derivatives are Bounded and Applications in Numerical Integration and for Special Means. RGMIA research report collection, 2 (1).
The publisher’s official version can be found at
Note that access to this version may require subscription.
Downloaded from VU Research Repository https://vuir.vu.edu.au/17139/
!
!
! Ê
¼
!"# Ê "#
¼
½
!$
¾
¼
"#
"#
"#
%
"#
"#
¼
½
"#
"#
& '( ) ' *+,- -./
0123101&1
14 556'57 1' !
'1 '1 1' 8 9'1 :
- ''
') "#' ' 1'
9'1 - ' ' ''
)'5' ; '
8 ) ; !
! Ê "#
¼
!"# Ê "#
¼
½
!$
¾
¼
"#
"#
"#"#%
"#% "#
4
"#
"4#
"#
%"#
%
%
4
¼
½
< %
"#$$$
%&'(#)&'($)* +#!))
= >'!
Ê-
"#!$
%
"
- !
"#
¼
"#
"44#
$
%
4
¼
"# %
4
¼
"#
$ "#
" "#% "##
4
%"#"# "#
"#
"#
¼
"#
"#
¼
"#
¼
½
"#
$
¼
½
%
4
%
4
$
¼
½
9 -
$
"# %
"#
$
4
"#
%"#
$
"#
%
%
4
1
?
%
4
$
"#
%
%
4
%
4
4
$
"#
%
4
%
4
8
$
4
"#
%"#
4
%
4
4
%
4
4
$
"#
%"#
%
%
4
'
"4#$< !" "#
"4#$$
#
"#
"#% "#
4
"#
"#
¼
½
"4#
$
"#
4
"#%
"#% "#
4
"#
"4#
"#
%
%
4
¼
½
% # &
"#
4
%
4
%
"#% "#
4
"#
"#
¼
½
"4@#
& ) 5' ; !
$ $
"#
"#% "#% "# "#
"4#
@
"#
%
%
4
¼
½
&'"
"#
"#%
%
4
% "# "#
"4A#
@
"#
¼
½
' -"4# -$
$
8
"4@#1' 1'-'/)
' -5' ; "4A#
8 ('
"#
! Ê "#
"# ! $
$
!$
$<
"# $
" Æ #%
" Æ #
"#
" Æ #$"Æ#
"
#%Æ
"#% "#
4
"4#
Æ < %Æ
Æ
$<B(
" Æ #
"#
¼
½
Æ
%"Æ#
%
%
4
:8'4
$<
"Æ# "
#%
"#% "#
4
Æ
·½
"#
Æ
%"Æ#
%
%
4
¼
½
Æ<
"$<# -
5'''< '"4#
) Æ$<
"# $" #%" #
"#
" #*"
" #!$
"
#
$<B
(+,-.)
" #
¼
½
%
%
4
"@#
) Æ$#
"# $
" #%
" #
"#
" ##
" #$
"#% "#
4
(
" #
¼
½
"A#
$
"# $" #%" #
"#
" # $
4
"
#
%
"
#% "
#
4
%
%
(
" #
¼
½
%
%
4
"#
"# $" #%" #
"<#
" #$
4
%
4
%
"
#% "
#
4
" #(
" #
¼
½
"#
&)5' ; '' /
'- >
$
"# $" #%" #
"4#
" # $ 4
"
#
%
"
#% "
#
%@
%@
" #(
" #
¼
½
@
%
%
4
"#
'"
"# $" #%" #
"#
" #$ 4
%
4
%
"
#% "
#
(
" #
@
¼
½
"@#
= 1 ' !
"#
$"#!$
"%#
4
<B
"-#
$"#!$
B <B
"1#
$"#!$
4
B<B
"#
$"#!$
$
$
<B
"#
$"#!$
$
½
$ B
"# /
$
"#!$
$
·½
·½
½
$
Ê <
8 /!
/ '11 ' $ $
9 1 "4#'!
"# "#%
"#% "#
4
"#
"#
"#
%"#
%
"#
¼
½
< 1
%
4
4
"# * ' !"<# "<# "#$
Ê<8 <
"#% "#
4
$"
#
"# $
"#
¼
½
$
" <
-"#1!
"#
%"
#
"#
"4#
"#
%"#
%
"#
"#
Æ
"#
Æ
"#!$
" <
<
%
"4# * ' !"<# "<# "#$
<7!
"#% "#
4
$
"#
"# $
"#
¼
½
$
-"#1 < %
!
"#%
"#
%"#
%
"#
"#
"#
"# * ' !"<# Ê "#$<7!
"#% "#
4
$
"# $
¼
½
$
-"#1
"#
%"#
%
"#
"#
"#
<
%
6 5 .8C9, 0
* D E 2E 3
*:C 0
* : . &9F /
F:1'12- 61/G /=
4 5 5 6C:H.C 5 7:9H :1 ; '
- ' 1' ''1 0 1
½½+2334) 256&253
!"#$%%&'
(
('))$
(
%.
/0