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Dergiler / Sakarya University Journal of Science / 2020 / Cilt: 24 Sayı: 4

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

Mahir KADAKAL
Sayfa
652–664
Yayın Tarihi
2020-08-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, results were obtained according to the special cases of α, m_1 and m_2.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:In addition, results were obtained according to the special cases of α, m_1 and m_2.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:(alpha m1 m2)-GA convex function · Hölder and power-mean inequalities · Hölder-İşcan inequality

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.

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Bu Makaleye Atıf Yap

KADAKAL, M. (2020). Some new inequalities for (α,m1,m2 )-GA convex functions. Sakarya University Journal of Science, Cilt: 24 Sayı: 4, 652–664. https://ajindex.com/articles/941904

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Kaynakça (4)

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  3. A.P. Ji, T.Y. Zhang, F. Qi, “Integral inequalities of Hermite-Hadamard type for (α,m)-GA-convex functions,” arXiv preprint arXiv:1306.0852, 4 June 2013. H. Kadakal, “Hermite-Hadamard type inequalities for trigonometrically convex functions,” Scientific Studies and Research. Series Mathematics and Informatics, 28(2), 19-28, 2018. H. Kadakal, “New Inequalities for Strongly r-Convex Functions,” Journal of Function Spaces, Volume 2019, Article ID 1219237, 10 pages, 2019. H. Kadakal, “(m_1,m_2 )-convexity and some new Hermite-Hadamard type inequalities,” International Journal of Mathematical Modelling and Computations, (Accepted for publication), 2020. H. Kadakal, “(α,m_1,m_2 )-convexity and some inequalities of Hermite-Hadamard type,” Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2128-2142, 2019. M. Kadakal, “(m_1,m_2 )-geometric arithmetically convex functions and related inequalities,” Mathematical Sciences and Applications E-Notes, (Submitted to journal), 2020.
  4. M. Kadakal, H. Kadakal and İ. İşcan, “Some new integral inequalities for n-times differentiable s-convex functions in the first sense,” Turkish Journal of Analysis and Number Theory, 5(2), 63-68, 2017. V.G. Miheşan, “A generalization of the