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Hadamard Integral Inequality for the Class of Harmonically (γ, η)-Convex Functions

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Frontiers in Functional Equations and Analytic Inequalities

Abstract

In this paper, harmonically (γ, η)-convex inequality is introduced as

$$\displaystyle \begin{aligned} f\left ( \frac {1}{\gamma _{\frac {1}{y},\frac {1}{x}}(t)}\right ) \leq \frac {1}{\eta _{\frac {1}{f(y)},\frac {1}{f(x)}}(t)}, \end{aligned} $$

in which γ and η are two geodesic arcs. Then, some refinements of Hadamard integral inequality for harmonically (γ, η)-convex functions in the case of Lebesgue and Sugeno integral are studied.

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Vosoughian, H., Abbaszadeh, S., Oraki, M. (2019). Hadamard Integral Inequality for the Class of Harmonically (γ, η)-Convex Functions. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_34

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