In this article, we obtain an extension of the classical Hermite-Hadamard inequality for convex functions (concave functions) extending it to the power functions
[
f
(
x
)
]
n
{[f\left(x)]}^{n}
. Some related inequalities are also introduced. By applying those results in analysis, we obtain new upper and lower bounds for the error function.
<abstract><p>This paper aims to investigate a new type of derivations in a fuzzy Banach algebra. Moreover, by using the fixed point method, we obtain some stability results of the hom-der in fuzzy Banach algebras associated with the functional equation</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ f(x+{\textbf{k}}y) = f(x)+{\textbf{k}}f(y) $\end{document} </tex-math></disp-formula></p>
<p>where $ {\textbf{k}} $ is a fixed positive integer greater than $ 1 $.</p></abstract>
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