JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HERMITE-HADAMARD TYPE INEQUALITIES FOR GEOMETRIC-ARITHMETICALLY s-CONVEX FUNCTIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HERMITE-HADAMARD TYPE INEQUALITIES FOR GEOMETRIC-ARITHMETICALLY s-CONVEX FUNCTIONS
Hua, Ju; Xi, Bo-Yan; Qi, Feng;
  PDF(new window)
 Abstract
In the paper, several properties of geometric-arithmetically s-convex functions are provided, an integral identity in which the integrands are products of a function and a derivative is found, and then some inequalities of Hermite-Hadamard type for integrals whose integrands are products of a derivative and a function whose derivative is of the geometric-arithmetic s-convexity are established.
 Keywords
property;identity;Hermite-Hadamard integral inequality;geometric-arithmetically s-convex function;
 Language
English
 Cited by
1.
Hermite–Hadamard-Type Integral Inequalities for Functions Whose First Derivatives are Convex, Ukrainian Mathematical Journal, 2015, 67, 4, 625  crossref(new windwow)
2.
Some New Generalized Integral Inequalities for GA-s-Convex Functions via Hadamard Fractional Integrals, Chinese Journal of Mathematics, 2016, 2016, 1  crossref(new windwow)
3.
Some new inequalities of Simpson type for strongly $$\varvec{s}$$ s -convex functions, Afrika Matematika, 2015, 26, 5-6, 741  crossref(new windwow)
4.
Hermite-Hadamard and Simpson Type Inequalities for DifferentiableP-GA-Functions, International Journal of Analysis, 2014, 2014, 1  crossref(new windwow)
5.
Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions, Journal of the Egyptian Mathematical Society, 2016, 24, 2, 175  crossref(new windwow)
6.
Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, Moroccan Journal of Pure and Applied Analysis, 2016, 2, 1  crossref(new windwow)
 References
1.
R.-F. Bai, F. Qi, and B.-Y. Xi, Hermite-Hadamard type inequalities for the m-and (${\alpha}$, m)-logarithmically convex functions, Filomat 26 (2013), no. 1, 1-7.

2.
S.-P. Bai and F. Qi, Some inequalities for ($s_1$, $m_1$)-($s_2$, $m_2$)-convex functions on the coordinates, Glob. J. Math. Anal. 1 (2013), no. 1, 22-28.

3.
S.-P. Bai, S.-H. Wang, and F. Qi, Some Hermite-Hadamard type inequalities for n-time differentiable (${\alpha}$, m)-convex functions, J. Inequal. Appl. 2012 (2012), Article 267, 11 pages. crossref(new window)

4.
L. Chun and F. Qi, Integral inequalities of Hermite-Hadamard type for functions whose 3rd derivatives are s-convex, Appl. Math. 3 (2012), no. 11, 1680-1685. crossref(new window)

5.
S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), no. 5, 91-95.

6.
S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Type Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.

7.
H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), no. 1, 100-111. crossref(new window)

8.
D. Y. Hwang, Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables, Appl. Math. Comput. 217 (2011), no. 23, 9598-9605. crossref(new window)

9.
I. Iscan, Hermite-Hadamard type inequalities for s-GA-convex functions, available online at http://arxiv.org/abs/1306.1960.

10.
A.-P. Ji, T.-Y. Zhang, and F. Qi, Integral inequalities of Hermite-Hadamard type for (${\alpha}$, m)-GA-convex functions, http://arxiv.org/abs/1306.0852.

11.
W.-D. Jiang, D.-W. Niu, Y. Hua, and F. Qi, Generalizations of Hermite-Hadamard inequality to n-time differentiable functions which are s-convex in the second sense, Analysis (Munich) 32 (2012), no. 3, 209-220.

12.
U. S. Kirmaci, M. K. Bakula, M. E. Ozdemir, and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (2007), no. 1, 26-35. crossref(new window)

13.
C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2000), no. 2, 155-167.

14.
C. P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (2003), no. 4, 571-579.

15.
C. P. Niculescu and L.-E. Persson, Convex Functions and Their Applications, CMS Books in Mathematics, Springer-Verlag, 2005.

16.
F. Qi, Z.-L. Wei, and Q. Yang, Generalizations and refinements of Hermite-Hadamard's inequality, Rocky Mountain J. Math. 35 (2005), no. 1, 235-251. crossref(new window)

17.
M. Z. Sarikaya, E. Set, and M. E. Ozdemir, On new inequalities of Simpson's type for s-convex functions, Comput. Math. Appl. 60 (2010), no. 8, 2191-2199. crossref(new window)

18.
Y. Shuang, H.-P. Yin, and F. Qi, Hermite-Hadamard type integral inequalities for geometric-arithmetically s-convex functions, Analysis (Munich) 33 (2013), no. 2, 197-208.

19.
K. L. Tseng, S. R. Hwang, G. S. Yang, and J. C. Lo, Two inequalities for differentiable mappings and applications to weighted trapezoidal formula, weighted midpoint formula and random variable, Math. Comput. Modelling 53 (2011), no. 1-2, 179-188. crossref(new window)

20.
S.-H. Wang, B.-Y. Xi, and F. Qi, On Hermite-Hadamard type inequalities for (${\alpha}$, m)- convex functions, Int. J. Open Probl. Comput. Sci. Math. 5 (2012), no. 4, 47-56. crossref(new window)

21.
S.-H. Wang, B.-Y. Xi, and F. Qi, Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich) 32 (2012), no. 3, 247-262.

22.
B.-Y. Xi, R.-F. Bai, and F. Qi, Hermite-Hadamard type inequalities for the m- and (${\alpha}$, m)-geometrically convex functions, Aequationes Math. 84 (2012), no. 3, 261-269. crossref(new window)

23.
B.-Y. Xi, J. Hua, and F. Qi, Hermite-Hadamard type inequalities for extended s-convex functions on the coordinates in a rectangle, J. Appl. Anal. 20 (2014), no. 1, in press.

24.
B.-Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl. 2012 (2012), Article ID 980438, 14 pages.

25.
B.-Y. Xi and F. Qi, Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl. 18 (2013), no. 2, 163-176.

26.
B.-Y. Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat. 42 (2013), no. 3, 243-257.

27.
B.-Y. Xi and F. Qi, Some inequalities of Hermite-Hadamard type for h-convex functions, Adv. Inequal. Appl. 2 (2013), no. 1, 1-15.

28.
B.-Y. Xi, S.-H. Wang, and F. Qi, Some inequalities of Hermite-Hadamard type for functions whose 3rd derivatives are P-convex, Appl. Math. 3 (2012), no. 12, 1898-1902. crossref(new window)

29.
T.-Y. Zhang, A.-P. Ji, and F. Qi, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Matematiche (Catania) 68 (2013), no. 1, 229-239.