Research Article
BibTex RIS Cite

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

Year 2016, Volume: 45 Issue: 2, 381 - 390, 01.04.2016

Abstract

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

References

  • Abramowitz M. and Stegun I.A. (Eds.) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965).
  • 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.
  • Hudzik, H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math. 48, 100-111, 1994.
  • İşcan, İ. A new generalization of some integral inequalities for (α, m)-convex functions, Mathematical Sciences 7 (22), 1-8, 2013.
  • İşcan, İ. New estimates on generalization of some integral inequalities for (α, m)-convex functions, Contemp. Anal. Appl. Math. 1 (2), 253-264, 2013.
  • 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.
  • İşcan, İ. Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. 43(6), 935-942, 2014.
  • Miheşan, V. G. A generalization of the convexity, Seminer on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania,1993.
  • Ozdemir, M. E., Avcı, M. and Kavurmacı, H. Hermite-Hadamard-type inequalities via (α, m)-convexity, Comput. Math. Appl. 61, 2614-2620, 2011.
  • Ozdemir, M. E., Kavurmacı, H. and Set, E. Ostrowski’s type inequalities for (α, m)-convex functions, Kyungpook Math. J. 50, 371-378, 2010.
  • Ozdemir, M. E., Set, E. and Sarıkaya, M. Z. Some new Hadamard’s type inequalities for co-ordinated m-convex and (α, m)-convex functions, Hacet. J. Math. Stat. 40 (2), 219-229, 2011.
  • Set, E., Sardari, M., Ozdemir, M. E. and Rooin, J. On generalizations of the Hadamard inequality for (α, m)-convex functions, RGMIA Res. Rep. Coll. 12 (4), Article 4, 2009.
Year 2016, Volume: 45 Issue: 2, 381 - 390, 01.04.2016

Abstract

References

  • Abramowitz M. and Stegun I.A. (Eds.) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965).
  • 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.
  • Hudzik, H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math. 48, 100-111, 1994.
  • İşcan, İ. A new generalization of some integral inequalities for (α, m)-convex functions, Mathematical Sciences 7 (22), 1-8, 2013.
  • İşcan, İ. New estimates on generalization of some integral inequalities for (α, m)-convex functions, Contemp. Anal. Appl. Math. 1 (2), 253-264, 2013.
  • 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.
  • İşcan, İ. Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. 43(6), 935-942, 2014.
  • Miheşan, V. G. A generalization of the convexity, Seminer on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania,1993.
  • Ozdemir, M. E., Avcı, M. and Kavurmacı, H. Hermite-Hadamard-type inequalities via (α, m)-convexity, Comput. Math. Appl. 61, 2614-2620, 2011.
  • Ozdemir, M. E., Kavurmacı, H. and Set, E. Ostrowski’s type inequalities for (α, m)-convex functions, Kyungpook Math. J. 50, 371-378, 2010.
  • Ozdemir, M. E., Set, E. and Sarıkaya, M. Z. Some new Hadamard’s type inequalities for co-ordinated m-convex and (α, m)-convex functions, Hacet. J. Math. Stat. 40 (2), 219-229, 2011.
  • Set, E., Sardari, M., Ozdemir, M. E. and Rooin, J. On generalizations of the Hadamard inequality for (α, m)-convex functions, RGMIA Res. Rep. Coll. 12 (4), Article 4, 2009.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

İmdat İşcan

Publication Date April 1, 2016
Published in Issue Year 2016 Volume: 45 Issue: 2

Cite

APA İşcan, İ. (2016). Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics, 45(2), 381-390.
AMA İşcan İ. Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics. April 2016;45(2):381-390.
Chicago İşcan, İmdat. “Hermite-Hadamard Type Inequalities for Harmonically (α, M)-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 45, no. 2 (April 2016): 381-90.
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 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, 2016.
ISNAD İşcan, İmdat. “Hermite-Hadamard Type Inequalities for Harmonically (α, M)-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 45/2 (April 2016), 381-390.
JAMA 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, 2016, pp. 381-90.
Vancouver İşcan İ. Hermite-Hadamard type inequalities for harmonically (α, m)-convex functions. Hacettepe Journal of Mathematics and Statistics. 2016;45(2):381-90.