BibTex RIS Kaynak Göster

Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications

Yıl 2013, Cilt: 42 Sayı: 3, 243 - 257, 01.03.2013

Öz

In the paper, the authors offer some new inequalities for differentiableconvex functions, which are connected with Hermite-Hadamard integralinequality, and apply these inequalities to special means of two positivenumbers.

Kaynakça

  • Bai, R.-F., Qi, F. and Xi, B.-Y. Hermite-Hadamard type inequalities for the m- and (α, m)logarithmically convex functions, Filomat 27 (1), 1–7, 2013.
  • Dragomir, S. S. and Agarwal, R. P. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (5), 91–95, 1998.
  • Dragomir, S. S., Agarwal, R. P. and Cerone, P. On Simpson’s inequality and applications, J. Inequal. Appl. 5 (6), 533–579, 2000.
  • Kirmaci, U. S. Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput. 147 (1), 137–146, 2004. Mitrinovi´ c, D. S. Analytic Inequalities, Springer-Verlag, Berlin, 1970.
  • Pearce, C. E. M. and Peˇ cari´ c, J. Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett. 13 (2), 51–55, 2000.
  • Qi, F. Bounds for the ratio of two gamma functions, J. Inequal. Appl. 2010, Article ID 493058, 84 pages, 2010.
  • Qi, F., Wei, Z.-L. and Yang, Q. Generalizations and refinements of Hermite-Hadamard’s inequality, Rocky Mountain J. Math. 35 (1), 235–251, 2005.
  • Wang, S.-H., Xi, B.-Y. and Qi, F. On Hermite-Hadamard type inequalities for (α, m)-convex functions, Int. J. Open Probl. Comput. Sci. Math. 5 (4), 47–56, 2012.
  • Wang, S.-H., Xi, B.-Y. and Qi, F. Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich) 32 (3), 247–262, 20 Xi, B.-Y., Bai, R.-F. and Qi, F. Hermite-Hadamard type inequalities for the m- and (α, m)geometrically convex functions, Aequationes Math. 84 (3), 261–269, 2012.
  • Xi, B.-Y. and Qi, F. Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl. 2012, Article ID 980438, 14 pages, 20

Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications

Yıl 2013, Cilt: 42 Sayı: 3, 243 - 257, 01.03.2013

Öz

-

Kaynakça

  • Bai, R.-F., Qi, F. and Xi, B.-Y. Hermite-Hadamard type inequalities for the m- and (α, m)logarithmically convex functions, Filomat 27 (1), 1–7, 2013.
  • Dragomir, S. S. and Agarwal, R. P. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (5), 91–95, 1998.
  • Dragomir, S. S., Agarwal, R. P. and Cerone, P. On Simpson’s inequality and applications, J. Inequal. Appl. 5 (6), 533–579, 2000.
  • Kirmaci, U. S. Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput. 147 (1), 137–146, 2004. Mitrinovi´ c, D. S. Analytic Inequalities, Springer-Verlag, Berlin, 1970.
  • Pearce, C. E. M. and Peˇ cari´ c, J. Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett. 13 (2), 51–55, 2000.
  • Qi, F. Bounds for the ratio of two gamma functions, J. Inequal. Appl. 2010, Article ID 493058, 84 pages, 2010.
  • Qi, F., Wei, Z.-L. and Yang, Q. Generalizations and refinements of Hermite-Hadamard’s inequality, Rocky Mountain J. Math. 35 (1), 235–251, 2005.
  • Wang, S.-H., Xi, B.-Y. and Qi, F. On Hermite-Hadamard type inequalities for (α, m)-convex functions, Int. J. Open Probl. Comput. Sci. Math. 5 (4), 47–56, 2012.
  • Wang, S.-H., Xi, B.-Y. and Qi, F. Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich) 32 (3), 247–262, 20 Xi, B.-Y., Bai, R.-F. and Qi, F. Hermite-Hadamard type inequalities for the m- and (α, m)geometrically convex functions, Aequationes Math. 84 (3), 261–269, 2012.
  • Xi, B.-Y. and Qi, F. Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl. 2012, Article ID 980438, 14 pages, 20
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Matematik
Yazarlar

Bo-Yan Xi Bu kişi benim

Feng Qi Bu kişi benim

Yayımlanma Tarihi 1 Mart 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 42 Sayı: 3

Kaynak Göster

APA Xi, B.-Y., & Qi, F. (2013). Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications. Hacettepe Journal of Mathematics and Statistics, 42(3), 243-257.
AMA Xi BY, Qi F. Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications. Hacettepe Journal of Mathematics and Statistics. Mart 2013;42(3):243-257.
Chicago Xi, Bo-Yan, ve Feng Qi. “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”. Hacettepe Journal of Mathematics and Statistics 42, sy. 3 (Mart 2013): 243-57.
EndNote Xi B-Y, Qi F (01 Mart 2013) Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications. Hacettepe Journal of Mathematics and Statistics 42 3 243–257.
IEEE B.-Y. Xi ve F. Qi, “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”, Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 3, ss. 243–257, 2013.
ISNAD Xi, Bo-Yan - Qi, Feng. “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”. Hacettepe Journal of Mathematics and Statistics 42/3 (Mart 2013), 243-257.
JAMA Xi B-Y, Qi F. Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications. Hacettepe Journal of Mathematics and Statistics. 2013;42:243–257.
MLA Xi, Bo-Yan ve Feng Qi. “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”. Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 3, 2013, ss. 243-57.
Vancouver Xi B-Y, Qi F. Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications. Hacettepe Journal of Mathematics and Statistics. 2013;42(3):243-57.