# On Hadamard-Type Inequalities Involving Several Kinds of Convexity

@article{Set2010OnHI,
title={On Hadamard-Type Inequalities Involving Several Kinds of Convexity},
author={Erhan Set and M. Emin {\"O}zdemir and Sever Silvestru Dragomir},
journal={Journal of Inequalities and Applications},
year={2010},
volume={2010},
pages={1-12}
}
• Published 14 May 2010
• Mathematics
• Journal of Inequalities and Applications
We do not only give the extensions of the results given by Gill et al. (1997) for log-convex functions but also obtain some new Hadamard-type inequalities for log-convex -convex, and -convex functions.
54 Citations
On Hermite Hadamard-type inequalities for strongly log-convex functions
• Mathematics
• 2012
In this paper, the notation of strongly log-convex functions with respect to c>0 is introduced and versions of Hermite Hadamard-type inequalities for strongly logarithmic convex functions are
ON HERMITE HADAMARD INEQUALITIES FOR PRODUCT OF TWO log-'-CONVEX FUNCTIONS
In this paper, we introduce the notion of log-'-convex functions and present some properties and representation of such functions. We obtain some results of the Hermite Hadamard inequalities for
On Generalized Inequalities of Hermite-Hadamard Type for Convex Functions
• Mathematics
• 2017
In this paper, new integral inequalities of Hermite-Hadamard type are developed for n−times differentiable convex functions. Also a parallel development is made base on concavity.
On Iyengar-Type Inequalities via Quasi-Convexity and Quasi-Concavity
In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained
On Iyengar-Type Inequalities via Quasi-Convexity and Quasi-Concavity
In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained
The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results
• Mathematics
• 2011
Abstract In this paper, we establish Hermite-Hadamard type inequalities for s - convex functions in the second sense and m - convex functions via fractional integrals. The analysis used in the proofs
On new inequalities of Hermite Hadamard type for functions whose second derivatives in absolute value are s-convex
• Mathematics
• 2016
In this paper, we establish several inequalities of the right hand side of Hermite-Hadamard inequalities for functions whose second derivatives are s-convex in the second sense by using Holder and
Generalization of Favard’s and Berwald’s Inequalities for Strongly Convex Functions
• Mathematics
• 2019
In this paper, we give generalization of discrete weighted Favard’s and Berwald’s inequalities for strongly convex functions. The obtained results are the improvement and generalization of the
Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense via fractional integrals
• Mathematics
• 2013
In this paper we establish Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense and concave.
HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS
• Mathematics
• 2017
In this paper, we establish some fractional Hermite-Hadamard type inequalities for harmonically $(\alpha,m)$-convex functions. Also, we give some applications to special means of positive real

## References

SHOWING 1-10 OF 22 REFERENCES
On The Hadamard's Inequality for Log-Convex Functions on the Coordinates
• Mathematics
• 2009
Inequalities of the Hadamard and Jensen types for coordinated log-convex functions defined in a rectangle from the plane and other related results are given.
Hadamard Type Inequalities for m-Convex and ({\alpha},m)-Convex Functions via Fractional Integrals
• Mathematics
• 2012
In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m-convex and ({\alpha},m)-convex functions via Riemann-Liouville
A note on integral inequalities involving Two Log-Convex Functions
The main aim of the present note is to establish new Hadmard like integral inequalities involving two log-convex functions. Mathematics subject classification (2000): 26D15, 26D99.
The Hermite-Hadamard Type Inequality of GA-Convex Functions and Its Application
• Mathematics
• 2010
We established a new Hermit-Hadamard type inequality for GA-convex functions. As applications, we obtain two new Gautschi type inequalities for gamma function.
• Mathematics
• 1997
Abstract Versions of the upper Hadamard inequality are developed for r -convex and r -concave functions.
HADAMARD TYPE INEQUALITIES FOR M-CONVEX AND (ALPHA, M)-CONVEX FUNCTIONS
• Mathematics
• 2008
In this paper we establish several Hadamard type inequalities for differentiable m-convex and (α , m)-convex functions. We also establish Hadamard type inequalities for products of two m-convex or (α
On the Hermite-Hadamard Inequality and Other Integral Inequalities Involving Two Functions
• Mathematics
• 2010
We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is
A direct proof of the s-Hölder continuity of Breckner s-convex functions
Summary. We give a direct proof of W. W. Breckner's result that Breckner s-convex real-valued functions on finite dimensional normed spaces are locally s-Hölder.