Research Article

Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions

Volume: 45 Number: 2 April 1, 2016
EN

Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions

Abstract

The author introduces the concept of harmonically (α, m)-convex functions and establishes some Hermite-Hadamard type inequalities of these classes of functions.

Keywords

References

  1. Abramowitz M. and Stegun I.A. (Eds.) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965).
  2. Bakula, M.K., Ozdemir, M. E. and Pecaric, J. Hadamard type inequalities for m-convex and (α, m)-convex functions, J. Inequal. Pure Appl. Math. 9 (4), Article 96, p. 12, 2008.
  3. Hudzik, H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math. 48, 100-111, 1994.
  4. İşcan, İ. A new generalization of some integral inequalities for (α, m)-convex functions, Mathematical Sciences 7 (22), 1-8, 2013.
  5. İşcan, İ. New estimates on generalization of some integral inequalities for (α, m)-convex functions, Contemp. Anal. Appl. Math. 1 (2), 253-264, 2013.
  6. İşcan, İ. Hermite-Hadamard type inequalities for functions whose derivatives are (α, m)- convex, International Journal of Engineering and Applied sciences 2 (3), 69-78, 2013.
  7. İşcan, İ. Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. 43(6), 935-942, 2014.
  8. Miheşan, V. G. A generalization of the convexity, Seminer on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania,1993.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

April 1, 2016

Submission Date

May 23, 2013

Acceptance Date

August 6, 2014

Published in Issue

Year 2016 Volume: 45 Number: 2

APA
İşcan, İ. (2016). Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics, 45(2), 381-390. https://izlik.org/JA57MN43JL
AMA
1.İşcan İ. Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics. 2016;45(2):381-390. https://izlik.org/JA57MN43JL
Chicago
İşcan, İmdat. 2016. “Hermite-Hadamard Type Inequalities for Harmonically (α, M)-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 45 (2): 381-90. https://izlik.org/JA57MN43JL.
EndNote
İşcan İ (April 1, 2016) Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics 45 2 381–390.
IEEE
[1]İ. İşcan, “Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, pp. 381–390, Apr. 2016, [Online]. Available: https://izlik.org/JA57MN43JL
ISNAD
İşcan, İmdat. “Hermite-Hadamard Type Inequalities for Harmonically (α, M)-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 45/2 (April 1, 2016): 381-390. https://izlik.org/JA57MN43JL.
JAMA
1.İşcan İ. Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics. 2016;45:381–390.
MLA
İşcan, İmdat. “Hermite-Hadamard Type Inequalities for Harmonically (α, M)-Convex Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, Apr. 2016, pp. 381-90, https://izlik.org/JA57MN43JL.
Vancouver
1.İmdat İşcan. Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics [Internet]. 2016 Apr. 1;45(2):381-90. Available from: https://izlik.org/JA57MN43JL