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GENERALISATIONS OF INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE THROUGH CONVEXITY

Part of: Real functions Inequalities

Published online by Cambridge University Press:  20 December 2012

MUHAMMAD MUDDASSAR ,
MUHAMMAD IQBAL BHATTI  and
WAJEEHA IRSHAD
MUHAMMAD MUDDASSAR*
Affiliation:
Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan
MUHAMMAD IQBAL BHATTI
Affiliation:
Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan email uetzone@hotmail.com
WAJEEHA IRSHAD
Affiliation:
Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan email wchattah@hotmail.com
*
✉malik.muddassar@gmail.com
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Abstract

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In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite–Hadamard integral inequality for mappings whose derivatives are $s$-$(\alpha , m)$-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.

Keywords

Hermite–Hadamard type inequalitys-( α, m)-convex functionp-logarithmic meanHölder’s integral inequalitytrapezoidal formulaspecial means

MSC classification

Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 26D15: Inequalities for sums, series and integrals 26A51: Convexity, generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 320 - 330
Copyright
Copyright ©2012 Australian Mathematical Publishing Association Inc. 

References

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