New Ostrowski type inequalities for GA-convex functions

Year 2016, Volume: 4 Issue: 4, 1 - 11, 31.12.2016

Hüsnü Anıl Çoban , İmdat Iscan Mehmet Kunt

https://izlik.org/JA75JY58RA

Abstract

In this work, we reveal a new equality for differentiable functions. By using this equality, we have some new Ostrowki type inequalities and some error estimates for the midpoint formula for functions whose derivatives in absolute values at certain powers are GA-convex.

Keywords

Ostrowski type inequalities , midpoint type inequalities

References

• M. Alomari,M. Darus, Some Ostrowski’s type inequalities for convex functions with applications, RGMIA Res.Rep. Collect., 13(1) (2010), Article 3, 1-14.
• S. S. Dragomir, T. M. Rassias, Ostrowski type inequalities and applications in numerical integration, Kluwer Academic Publishers, 2002.
• I. Iscan, Hermite-Hadamard type inequalities for GA-s-convex functions,Le Matematiche, Vol. LXIX (2014) 129-146.
• I. Iscan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp Jurnal of Mathematics, Volume 3, No 1 (2015) 63-74.
• I. Iscan, S. Numan, Ostrowski type inequalities for harmonically quasi-convex functions, Elect. J. Math. Anal. App., 2(2) (2014) 189-198.
• C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155–167.
• A. Ostrowski, ¨Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert. Comment. Math. Hel, 10 (1938), 226–227.
• M. E. ¨Ozdemir, C¸ . Yıldız, New Ostrowski Type Inequalities for Geometrically Convex Functions, Int. J. Modern Math. Sci., 8(1) (2013) 27-35.
• E. Set, M. E. ¨Ozdemir, M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Uni. Ser. Math. Inform. 27(1) (2012) 67-82.