Araştırma Makalesi
BibTex RIS Kaynak Göster

OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS

Yıl 2015, Cilt: 3 Sayı: 1, 63 - 74, 01.04.2015

İmdat İşcan

Öz

The author introduces the concept of harmonically s-convex functions and establishes some Ostrowski type inequalities and a variant of Hermite- Hadamard inequality for these classes of functions.

Anahtar Kelimeler

Harmonically s-convex function Ostrowski type inequality Hermite- Hadamard's inequality hypergeometric function

Kaynakça

  • [1] M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
  • [2] M. Alomari, M. Darus, S. S. Dragomir, and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett. 23 (1) (2010), 1071-1076.
  • [3] M. W. Alomari, M. Darus, and U. S. Kirmaci, Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Math. Sci. B31, no.4 (2011), 1643{1652.
  • [4] M. Avci, H. Kavurmaci and M. Emin  Ozdemir, New inequalities of Hermite{Hadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput. 217 (2011) 5171{5176.
  • [5] S.S. Dragomir, S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4) (1999), 687{696.
  • [6] S. Hussain, M. I. Bhatti, and M. Iqbal, Hadamard-type inequalities for s-convex functions I, J. Math., Punjab Univ. 41 (2009), 51{60.
  • [7] H. Hudzik , L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100{111.
  • [8] İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math. 86, No.4 (2013), 727-746.
  • [9] İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Vol: 43 (6) (2014), 935-942.
  • [10] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals, Applicable Analysis, vol. 93, issue 9 (2014), 1846-1862.
  • [11] U. S. Kirmaci, M. Klaricic Bakula, M.E.  Ozdemir, and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193, no.1 (2007), 26{35.
  • [12] Z. Liu, A note on Ostrowski type inequalities related to some s-convex functions in the second sense, Bull. Korean Math. Soc. 49 (4) (2012), 775-785. Available online at http://dx.doi.org/10.4134/BKMS.2012.49.4.775.
  • [13] A. Ostrowski, Uber die Absolutabweichung einer di erentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv. 10 (1938) 226{227.

Yıl 2015, Cilt: 3 Sayı: 1, 63 - 74, 01.04.2015

İmdat İşcan

Öz

Kaynakça

  • [1] M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
  • [2] M. Alomari, M. Darus, S. S. Dragomir, and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett. 23 (1) (2010), 1071-1076.
  • [3] M. W. Alomari, M. Darus, and U. S. Kirmaci, Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Math. Sci. B31, no.4 (2011), 1643{1652.
  • [4] M. Avci, H. Kavurmaci and M. Emin  Ozdemir, New inequalities of Hermite{Hadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput. 217 (2011) 5171{5176.
  • [5] S.S. Dragomir, S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4) (1999), 687{696.
  • [6] S. Hussain, M. I. Bhatti, and M. Iqbal, Hadamard-type inequalities for s-convex functions I, J. Math., Punjab Univ. 41 (2009), 51{60.
  • [7] H. Hudzik , L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100{111.
  • [8] İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math. 86, No.4 (2013), 727-746.
  • [9] İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Vol: 43 (6) (2014), 935-942.
  • [10] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals, Applicable Analysis, vol. 93, issue 9 (2014), 1846-1862.
  • [11] U. S. Kirmaci, M. Klaricic Bakula, M.E.  Ozdemir, and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193, no.1 (2007), 26{35.
  • [12] Z. Liu, A note on Ostrowski type inequalities related to some s-convex functions in the second sense, Bull. Korean Math. Soc. 49 (4) (2012), 775-785. Available online at http://dx.doi.org/10.4134/BKMS.2012.49.4.775.
  • [13] A. Ostrowski, Uber die Absolutabweichung einer di erentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv. 10 (1938) 226{227.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

İmdat İşcan

Yayımlanma Tarihi 1 Nisan 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

APA İşcan, İ. (2015). OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS. Konuralp Journal of Mathematics, 3(1), 63-74.
AMA İşcan İ. OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS. Konuralp J. Math. Nisan 2015;3(1):63-74.
Chicago İşcan, İmdat. “OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY S-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics 3, sy. 1 (Nisan 2015): 63-74.
EndNote İşcan İ (01 Nisan 2015) OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS. Konuralp Journal of Mathematics 3 1 63–74.
IEEE İ. İşcan, “OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS”, Konuralp J. Math., c. 3, sy. 1, ss. 63–74, 2015.
ISNAD İşcan, İmdat. “OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY S-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics 3/1 (Nisan 2015), 63-74.
JAMA İşcan İ. OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS. Konuralp J. Math. 2015;3:63–74.
MLA İşcan, İmdat. “OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY S-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics, c. 3, sy. 1, 2015, ss. 63-74.
Vancouver İşcan İ. OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS. Konuralp J. Math. 2015;3(1):63-74.
 Kapak Resmi İndir
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.