Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2016, Cilt: 45 Sayı: 2, 381 - 390, 01.04.2016

İmdat İşcan

Öz

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

Anahtar Kelimeler

Harmonically (α m)-convex function Hermite-Hadamard type inequalities Hypergeometric function

Kaynakça

  • 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.

Yıl 2016, Cilt: 45 Sayı: 2, 381 - 390, 01.04.2016

İmdat İşcan

Öz

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

İmdat İşcan

Yayımlanma Tarihi 1 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 45 Sayı: 2

Kaynak Göster

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. Nisan 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, sy. 2 (Nisan 2016): 381-90.
EndNote İşcan İ (01 Nisan 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, c. 45, sy. 2, ss. 381–390, 2016.
ISNAD İşcan, İmdat. “Hermite-Hadamard Type Inequalities for Harmonically (α, M)-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 45/2 (Nisan 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, c. 45, sy. 2, 2016, ss. 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.

https://dergipark.org.tr/en/pub/hujms