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

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.