1Mathematics, College of Engineering & Science, Victoria University,
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 63-78
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Sever S. Dragomir; Sever S. Dragomir. A functional generalization of Ostrowski inequality via Montgomery identity. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 63-78. http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a6/
@article{AMUC_2015_84_1_a6,
author = {Sever S. Dragomir and Sever S. Dragomir},
title = { A functional generalization of {Ostrowski} inequality via {Montgomery} identity},
journal = {Acta mathematica Universitatis Comenianae},
pages = {63--78},
year = {2015},
volume = {84},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a6/}
}
TY - JOUR
AU - Sever S. Dragomir
AU - Sever S. Dragomir
TI - A functional generalization of Ostrowski inequality via Montgomery identity
JO - Acta mathematica Universitatis Comenianae
PY - 2015
SP - 63
EP - 78
VL - 84
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a6/
ID - AMUC_2015_84_1_a6
ER -
%0 Journal Article
%A Sever S. Dragomir
%A Sever S. Dragomir
%T A functional generalization of Ostrowski inequality via Montgomery identity
%J Acta mathematica Universitatis Comenianae
%D 2015
%P 63-78
%V 84
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a6/
%F AMUC_2015_84_1_a6
We show in this paper amongst other that, if $f : [a; b] \to R$ isabsolutely continuous on [a; b] and $\Phi : R \to R$ is convex (concave) on R then$$\Phi (f (x)-\frac{1}{b-a}\int_a^b f(t) dt \leq (\geq )\frac{1}{b-a}[\int_a^b \Phi[(t-a)f'(t)]dt-\int_a^b \Phi[(t-b)f'(t)]dt]$$for any $x \in[a; b]$.Natural applications for power and exponential functions are provided as well. Bounds for the Lebesgue p-norms of the deviation of a function from itsintegral mean are also given.
