Polynomial Inequalities with an Exponential Weight on (0,+∞)

We consider the weight \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{u(x) = x^{\gamma} e^{-x^{-\alpha}-x^{\beta}}}}$$\end{document} , with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{x \in(0,+\infty)}}$$\end{document} , α >  0, β >  1 and γ ≥  0 and prove Remez-, Bernstein–Markoff-, Schurand Nikolskii-type inequalities for algebraic polynomials with the weight u on (0, + ∞).