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MathCraft: PDF to LaTeX file: Sample-01

9 Hits, Last modified: 5 months ago

i% \else\svfootnotetext[#1]{#2}\fi% \fi } \begin{document} \maketitle ABSTRACT. We give a simple p... similar means of Stolarsky type. \vspace{10mm} \begin{center} {\large\textbf{1. Introduction and Prelim... ce{2mm} Let us consider the following means $$ \begin{aligned} & E(x, y ; r, s)=\left\{\dfrac{r\left(y^... s$ i.e. for $r \leq u$ and $s \leq v$, we have \begin{equation*} E(x, y ; r, s) \leq E(x, y ; u, v) . \

MathCraft: PDF to LaTeX file: Sample-02

5 Hits, Last modified: 5 months ago

Hadamard integral inequality } \author{} \date{} \begin{document} \maketitle \vspace{-0.7 in} If $f:[a,... ht), f_{+}^{\prime}\left(x_{0}\right)\right]$. \begin{wrapfigure}{r}{0.45\textwidth} \includegraphics[... tegrating both inequalities between $a$ and $b$ \begin{equation*} \int_{a}^{b} r(x) d x \leq \int_{a}^{b... }^{b} s(x) d x . \tag{1} \end{equation*} Now $$ \begin{aligned} \int_{a}^{b} r(x) d x & =\int_{a}^{b}\le