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HADAMARD INEQUALITIES FOR WRIGHT-CONVEX FUNCTIONS

HADAMARD INEQUALITIES FOR WRIGHT-CONVEX FUNCTIONS DEMONSTRATIO MATHEMATICAVol. XXXVIINo 32004K.-L. Tseng, G.-S. Yang, S. S. DragomirH A D A M A R D INEQUALITIES FOR WRIGHT-CONVEXFUNCTIONSAbstract. In this paper we establish several inequalities of Hadamard's type forWright-convex functions.1. IntroductionIf / : [a, 6] —• R is a convex function, thenis known as the Hadamard inequality ([5]).For some results which generalize, improve, and extend this famous integral inequality see [1] - [8], [10] - [15].In [2], Dragomir established the following theorem which is a refinementof the first inequality of (1.1).THEOREM 1.[0,1] by(1.2)If f : [a, b] —> R is a convex function, and H is defined onH i t ) = rL - l f ( t x + (1 - t)dx,then H is convex, increasing on [0,1], and for all t 6 [0,1], we have(1.3)/= H (0) < H (t) < H (1) =J / (x) dx.In [10], Yang and Hong established the following theorem which is arefinement of the second inequality of (1.1).Key words and phrases: Trapezoid inequality, Monotonic mappings, r—moment andthe expectation of a continuous random variable, the Beta mapping.1991 Mathematics Subject Classification: Primary: 26D15; Secondary: 41A55526K.-L. Tseng, G.-S. Yang, S. S. DragomirTHEOREM[0,1] by2. If f : [A, 6] —> M is a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

HADAMARD INEQUALITIES FOR WRIGHT-CONVEX FUNCTIONS

Tseng, K.-L.; Yang, G.-S.; Dragomir, S. S.
Demonstratio Mathematica , Volume 37 (3): 8 – Jul 1, 2004
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Publisher
de Gruyter
Copyright
© by K.-L. Tseng
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2004-0304
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXVIINo 32004K.-L. Tseng, G.-S. Yang, S. S. DragomirH A D A M A R D INEQUALITIES FOR WRIGHT-CONVEXFUNCTIONSAbstract. In this paper we establish several inequalities of Hadamard's type forWright-convex functions.1. IntroductionIf / : [a, 6] —• R is a convex function, thenis known as the Hadamard inequality ([5]).For some results which generalize, improve, and extend this famous integral inequality see [1] - [8], [10] - [15].In [2], Dragomir established the following theorem which is a refinementof the first inequality of (1.1).THEOREM 1.[0,1] by(1.2)If f : [a, b] —> R is a convex function, and H is defined onH i t ) = rL - l f ( t x + (1 - t)dx,then H is convex, increasing on [0,1], and for all t 6 [0,1], we have(1.3)/= H (0) < H (t) < H (1) =J / (x) dx.In [10], Yang and Hong established the following theorem which is arefinement of the second inequality of (1.1).Key words and phrases: Trapezoid inequality, Monotonic mappings, r—moment andthe expectation of a continuous random variable, the Beta mapping.1991 Mathematics Subject Classification: Primary: 26D15; Secondary: 41A55526K.-L. Tseng, G.-S. Yang, S. S. DragomirTHEOREM[0,1] by2. If f : [A, 6] —> M is a

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Demonstratio Mathematica – de Gruyter

Published: Jul 1, 2004

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