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BETTER BOUNDS FOR AN INEQUALITY OF THE OSTROWSKI TYPE WITH APPLICATIONS

BETTER BOUNDS FOR AN INEQUALITY OF THE OSTROWSKI TYPE WITH APPLICATIONS DEMONSTRATIO MATHEMATICAVol. XXXIVNo 32001N. S. Barnett, S. S. Dragomir, A. SofoB E T T E R B O U N D S F O R AN I N E Q U A L I T YOF T H E O S T R O W S K I T Y P E W I T H A P P L I C A T I O N SA b s t r a c t . In this paper we improve a recent result by Matic, Pecaric and Ujevic [6]and apply it for special means and cumulative probability functions.1. IntroductionIn 1938, A. Ostrowski (see [1] p. 468) proved the following inequalityi(1.1)br,n/_a+b\ 2-,ix — a + \(b -a)Mfor all x € [a, 6], provided that / is differentiate on (a,b) and |/'(i)| < Mfor all t £ (a, b).Using the following representation, which has been obtained by Montgomery in an equivalent form (see [1] p. 565)(1.2)/(*) - —66J f{t) dt = —\ p(x, t)f'(t)aadtfor all x G [a, 6], provided that / is absolutely continuous on [a, 6] and/p^( t - at ) := { t - bift€[a,x]2i f t e \ J )»M e W *we can put in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

BETTER BOUNDS FOR AN INEQUALITY OF THE OSTROWSKI TYPE WITH APPLICATIONS

Barnett, N. S.; Dragomir, S. S.; Sofo, A.
Demonstratio Mathematica , Volume 34 (3): 10 – Jul 1, 2001
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Publisher
de Gruyter
Copyright
© by N. S. Barnett
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2001-0304
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXIVNo 32001N. S. Barnett, S. S. Dragomir, A. SofoB E T T E R B O U N D S F O R AN I N E Q U A L I T YOF T H E O S T R O W S K I T Y P E W I T H A P P L I C A T I O N SA b s t r a c t . In this paper we improve a recent result by Matic, Pecaric and Ujevic [6]and apply it for special means and cumulative probability functions.1. IntroductionIn 1938, A. Ostrowski (see [1] p. 468) proved the following inequalityi(1.1)br,n/_a+b\ 2-,ix — a + \(b -a)Mfor all x € [a, 6], provided that / is differentiate on (a,b) and |/'(i)| < Mfor all t £ (a, b).Using the following representation, which has been obtained by Montgomery in an equivalent form (see [1] p. 565)(1.2)/(*) - —66J f{t) dt = —\ p(x, t)f'(t)aadtfor all x G [a, 6], provided that / is absolutely continuous on [a, 6] and/p^( t - at ) := { t - bift€[a,x]2i f t e \ J )»M e W *we can put in

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 2001

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