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

Hamid Vosoughian (), Sadegh Abbaszadeh () and Maryam Oraki ()
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Hamid Vosoughian: Semnan University, Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences
Sadegh Abbaszadeh: Paderborn University, Department of Computer Science
Maryam Oraki: Payame Noor University, Department of Mathematics

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 695-711 from Springer

Abstract: Abstract In this paper, harmonically (γ, η)-convex inequality is introduced as f 1 γ 1 y , 1 x ( t ) ≤ 1 η 1 f ( y ) , 1 f ( x ) ( t ) , $$\displaystyle \begin{aligned} f\left ( \frac {1}{\gamma _{\frac {1}{y},\frac {1}{x}}(t)}\right ) \leq \frac {1}{\eta _{\frac {1}{f(y)},\frac {1}{f(x)}}(t)}, \end{aligned} $$ 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.

Date: 2019
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DOI: 10.1007/978-3-030-28950-8_34

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