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MathCraft: PDF to LaTeX file: Sample-01

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i% \fi } \begin{document} \maketitle ABSTRACT. We give a simple proof of the Stolarsky means inequality as well as some related inequalities for similar means ... h $r$ and $s$ i.e. for $r \leq u$ and $s \leq v$, we have \begin{equation*} E(x, y ; r, s) \leq E(x,... end{equation*} \vspace{2mm} In this paper, first we shall give a simple proof of inequality (1). Furt

MathCraft: PDF to LaTeX file: Sample-02

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f(x) \leq s(x)$$ Integrating both inequalities between $a$ and $b$ \begin{equation*} \int_{a}^{b} r(x... b-a) . \end{aligned} $$ Using above value in (1), we have $$ f\left(\frac{a+b}{2}\right)(b-a) \leq \in