Some new inequalities for (α,m1,m2 )-GA convex functions

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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Volume: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 : 118 | Download : 16

Publication Date : 2020-08-01

Article Type : Research Paper

Abstract :In this manuscript, firstly we introduce and study the concept of insert ignore into journalissuearticles values(α,m_1,m_2 );-Geometric-Arithmetically insert ignore into journalissuearticles values(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

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