Some Ostrowski’s type inequalities for functions whose second derivatives are s-convex in the second sense

• Autorzy: Set E. , Sarikaya M. Z. , Ozdemir M. E.
• Języki publikacji: EN

Abstrakty

EN

Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.

Słowa kluczowe

EN

Ostrowski's inequality; convex function; s-convex functions

PL

nierówności Ostrowskiego; funkcja wypukła; funkcje s-wypukłe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 1
• Strony: 37--47
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Set E.

• Department of Mathematics Faculty of Science and Arts Ordu University Ordu, Turkey

autor

Sarikaya M. Z.

• Department of Mathematics Faculty of Science and Arts Düzce University Düzce, Turkey

autor

Ozdemir M. E.

• Atatürk University K.K. Education Faculty Department of Mathematics 25240, Campus, Erzurum, Turkey

Bibliografia

• [1] M. Alomari, M. Darus, Some Ostrowski’s type inequalities for convex functions with applications, RGMIA 13(1) (2010), Article 3. [ONLINE: http://ajmaa.org/RGMIA/v13n1.php]
• [2] M. Alomari, M. Darus, S. S. Dragomir, P. Cerone, Ostrowski’s inequalities for functions whose derivatives are s-convex in the second sense, RGMIA 12 (2009), Supp., No. 15.
• [3] P. Cerone, S. S. Dragomir J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Res. Rep. Coll. 1(1) (1998), Article 4.
• [4] S. S. Dragomir, S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl. Math. Lett. 11 (1998), 105–109.
• [5] M. Z. Sarıkaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenianae 79(1) (2010), 129–134.
• [6] E. Set, M. E. Özdemir, M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Unv. Ser. Math. Inform. 27(1) (2012), 67–82.
• [7] M. E. Özdemir, H. Kavurmaci, E. Set, Ostrowski’s type inequalities for (α, m)-convex functions, Kyungpook Math. J. 50 (2010), 371–378.
• [8] M. Z. Sarıkaya, E. Set, M. E. Özdemir, On the integral inequalities for mappings whose second dervatives are convex and applications, Stud. Univ. Babes–Bolyai Math., in press.
• [9] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), 13–20.
• [10] S. S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32(4) (1999), 687–696.
• [11] H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), 100–111.
• [12] A. Ostrowski,Über die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Helv. 10 (1938), 226–227.