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Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications

Year 2013, Volume: 42 Issue: 3, 243 - 257, 01.03.2013

Abstract

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.

References

  • 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

Year 2013, Volume: 42 Issue: 3, 243 - 257, 01.03.2013

Abstract

-

References

  • 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
There are 10 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Bo-Yan Xi This is me

Feng Qi This is me

Publication Date March 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 3

Cite

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. March 2013;42(3):243-257.
Chicago Xi, Bo-Yan, and Feng Qi. “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”. Hacettepe Journal of Mathematics and Statistics 42, no. 3 (March 2013): 243-57.
EndNote Xi B-Y, Qi F (March 1, 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 and F. Qi, “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 3, pp. 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 (March 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 and Feng Qi. “Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 3, 2013, pp. 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.