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MathCraft: PDF to LaTeX file: Sample-01
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es}}\end{center} \vspace{2mm} Let us consider the following means $$ \begin{aligned} & E(x, y ; r, s)=\left... , Stolarsky means. } \vspace{2mm} We consider the following function $f(x)=p^{2} \varphi_{r}(x)+2 p q \varph... mathbb{R}$. And therefore $\log$-convex. We need following lemma which proof can be found in [2]. \vspace{4... 2}, x_{1} \neq x_{2}, y_{1} \neq y_{2}$, then the following inequality is valid: \begin{equation*} \left(\d