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

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

Mahir KADAKAL
Pages
652–664
Publication Date
2020-08-01
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

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Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact:In addition, results were obtained according to the special cases of α, m_1 and m_2.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:(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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Cite This Article

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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References (4)

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