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ON SOME INTEGRAL INEQUALITIES FOR s;m -CONVEX FUNCTIONS

Yıl 2020, Cilt: 10 Sayı: 2, 288 - 295, 01.03.2020

B. Bayraktar M. Gürbüz

Öz

A new identity has been handled in this paper. It allows to derive new inequalities referring to upper estimation of the Jensen functional in the class of s, m - convex functions. Also some applications for special means are given by using new inequalities.

Anahtar Kelimeler

Convex function s m -convex Hermite-Hadamard inequalitiy H¨older inequality power mean inequality

Kaynakça

  • Dragomir, S. S., Agarwal, R. P., & Barnet, N. S. (2000) Inequalities for Beta and Gamma Functions via Some Classical and New Integral Inequalities. J. Ineq. Appl., 5, (2), 103-165.
  • Dragomir, S. S., & Pearce, C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs
  • Victoria University,[ONLINE. http://rgmia.org/papers/monographs/Master.pdf]. Breckner, W. W. (1978). Stetigkeitsaussagen f¨ur eine klasse verallgemeinerter konvexer funktionen in topologischen linearen r¨aumen. Publ. Inst. Math, 23 (37), 13-20.
  • Kirmaci, U. S. (2017), On Some Hermite-Hadamard Type Inequalities for Twice Differentiable (α, m)- convex functions and Applications. RGMIA Res. Rep. Coll., 20, Art. 51.
  • ¨Ozdemir, M. E., Avci, M., & H. Kavurmaci. (2011). Hermite-Hadamard-type Inequalities via (α, m)- convexity. Computer and Math. with Appl., 61, 2614-2620.
  • Park, J. (2011). Generalization of Ostrowski-type inequalities for differentiable real (s, m)-convex mappings. Far East J. of Math. Sci., 49(2), 157-171.
  • Park, J. (2011). Ostrowski type inequalities for mappings whose derivatives are (s, m) −convex in the second sense. Far East J. of Math. Sci., 49 (2), 181-195.
  • Sarikaya, M. Z., & Aktan, N. (2011). On the generalization of some integral inequalities and their applications. Math. and Comp. Modelling, 54, 2175-2182.
  • Set, E., Sardari, M., ¨Ozdemir, M. E., & Rooin, J. (2012). On Generalizations of the Hadamard
  • Inequality for (α, m)-Convex Functions. Kyungpook Math. J., 52, 307-317
  • Toader, G.H. (1984). Some Generalisations of the Convexity. Proc. Colloq. Approx. Optim, Cluj- Napoca, 329-338, Romania.
  • Dragomir, S.S. (2006). Bounds for the normalized Jensen functional. Bull. Aust. Math. Soc. 74(3), 476. uz

Yıl 2020, Cilt: 10 Sayı: 2, 288 - 295, 01.03.2020

B. Bayraktar M. Gürbüz

Öz

Kaynakça

  • Dragomir, S. S., Agarwal, R. P., & Barnet, N. S. (2000) Inequalities for Beta and Gamma Functions via Some Classical and New Integral Inequalities. J. Ineq. Appl., 5, (2), 103-165.
  • Dragomir, S. S., & Pearce, C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs
  • Victoria University,[ONLINE. http://rgmia.org/papers/monographs/Master.pdf]. Breckner, W. W. (1978). Stetigkeitsaussagen f¨ur eine klasse verallgemeinerter konvexer funktionen in topologischen linearen r¨aumen. Publ. Inst. Math, 23 (37), 13-20.
  • Kirmaci, U. S. (2017), On Some Hermite-Hadamard Type Inequalities for Twice Differentiable (α, m)- convex functions and Applications. RGMIA Res. Rep. Coll., 20, Art. 51.
  • ¨Ozdemir, M. E., Avci, M., & H. Kavurmaci. (2011). Hermite-Hadamard-type Inequalities via (α, m)- convexity. Computer and Math. with Appl., 61, 2614-2620.
  • Park, J. (2011). Generalization of Ostrowski-type inequalities for differentiable real (s, m)-convex mappings. Far East J. of Math. Sci., 49(2), 157-171.
  • Park, J. (2011). Ostrowski type inequalities for mappings whose derivatives are (s, m) −convex in the second sense. Far East J. of Math. Sci., 49 (2), 181-195.
  • Sarikaya, M. Z., & Aktan, N. (2011). On the generalization of some integral inequalities and their applications. Math. and Comp. Modelling, 54, 2175-2182.
  • Set, E., Sardari, M., ¨Ozdemir, M. E., & Rooin, J. (2012). On Generalizations of the Hadamard
  • Inequality for (α, m)-Convex Functions. Kyungpook Math. J., 52, 307-317
  • Toader, G.H. (1984). Some Generalisations of the Convexity. Proc. Colloq. Approx. Optim, Cluj- Napoca, 329-338, Romania.
  • Dragomir, S.S. (2006). Bounds for the normalized Jensen functional. Bull. Aust. Math. Soc. 74(3), 476. uz
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

B. Bayraktar Bu kişi benim

M. Gürbüz Bu kişi benim

Yayımlanma Tarihi 1 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 2

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