On hermite-hadamard type integral inequalities for n-times differentiable m- and (α, m)-logarithmically convex functions

M. A. Latif; S. S. Dragomir; E. Momoniat

doi:10.2298/FIL1611101L

On hermite-hadamard type integral inequalities for n-times differentiable m- and (α, m)-logarithmically convex functions

M. A. Latif, S. S. Dragomir, E. Momoniat

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper, we establish Hermite-Hadamard type inequalities for functions whose nth derivatives are m- and (α, m)-logarithmically convex functions. From our results, several results for classical trapezoidal and classical midpoint inequalities are obtained in terms second derivatives that are m- and (α, m)-logarithmically convex functions as special cases.

Original language	English
Pages (from-to)	3101-3114
Number of pages	14
Journal	Filomat
Volume	30
Issue number	11
DOIs	https://doi.org/10.2298/FIL1611101L
Publication status	Published - 2016
Externally published	Yes

Keywords

(α, m)-logarithmically convex function
Hermite-hadamard’s inequality
Hölder inequality
M-logarithmically convex function

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL1611101L

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AU - Dragomir, S. S.

AU - Momoniat, E.

PY - 2016

Y1 - 2016

N2 - In this paper, we establish Hermite-Hadamard type inequalities for functions whose nth derivatives are m- and (α, m)-logarithmically convex functions. From our results, several results for classical trapezoidal and classical midpoint inequalities are obtained in terms second derivatives that are m- and (α, m)-logarithmically convex functions as special cases.

AB - In this paper, we establish Hermite-Hadamard type inequalities for functions whose nth derivatives are m- and (α, m)-logarithmically convex functions. From our results, several results for classical trapezoidal and classical midpoint inequalities are obtained in terms second derivatives that are m- and (α, m)-logarithmically convex functions as special cases.

KW - (α, m)-logarithmically convex function

KW - Hermite-hadamard’s inequality

KW - Hölder inequality

KW - M-logarithmically convex function

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On hermite-hadamard type integral inequalities for n-times differentiable m- and (α, m)-logarithmically convex functions

Abstract

Keywords

ASJC Scopus subject areas

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