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}
}
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. 
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55 Citations
Background Citations
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55 Citations

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References

SHOWING 1-10 OF 22 REFERENCES
On some inequalities of Hermite-Hadamard type via m-convexity
On The Hadamard's Inequality for Log-Convex Functions on the Coordinates
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
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
We established a new Hermit-Hadamard type inequality for GA-convex functions. As applications, we obtain two new Gautschi type inequalities for gamma function.
Hadamard's Inequality forr-Convex Functions
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
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
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.
Hermite-Hadamard Inequality on Time Scales
We discuss some variants of the Hermite-Hadamard inequality for convex functions on time scales. Some improvements and applications are also included.
...
...