- Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 24 Issue: 4
- Some new inequalities for (α,m1,m2 )-GA convex functions
Some new inequalities for (α,m1,m2 )-GA convex functions
Authors : Mahir KADAKAL
Pages : 652-664
Doi:10.16984/saufenbilder.699212
View : 10 | Download : 5
Publication Date : 2020-08-01
Article Type : Other
Abstract :In this manuscript, firstly we introduce and study the concept of (α,m_1,m_2 )-Geometric-Arithmetically (GA) convex functions and some algebraic properties of such type functions. Then, we obtain Hermite-Hadamard type integral inequalities for the newly introduced class of functions by using an identity together with Hölder integral inequality, power-mean integral inequality and Hölder-İşcan integral inequality giving a better approach than Hölder integral inequality. Inequalities have been obtained with the help of Gamma function. In addition, results were obtained according to the special cases of α, m_1 and m_2.Keywords : (alpha m1 m2)-GA convex function, Hölder and power-mean inequalities, Hölder-İşcan inequality, Hermite-Hadamard integral inequality, power-mean inequality