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This question makes me wonder about more general inequalities, but I have a particular example. Let $C$ be a positive fixed constant, $0<\epsilon<1$ be given, and assume $\alpha,\beta\in ... 1answer 104 views Local positivity of solutions to linear differential inequalities (Chaplygin's theorem) According to the entry "Differential inequality" of the Encyclopedia of Mathematics http://www.encyclopediaofmath.org/index.php/Differential_inequality the following result is due to Chaplygin ... 0answers 130 views Upper bound on integrals of Legendre polynomials Hi, If$P_n(x) $is unnormalized shifted Legendre polynomial, and$g_{n,m}(x) = \int_0^x P_n(x_1)x_1^m dx_1, n>m $then what is the upper bound$ |g_{n,m} (x)|_{max} , x\in (0,1) $as a function ... 1answer 147 views An upper bound on a simple sum Hi, I am trying to put a bound on a sum. Given$\omega=\exp(2\pi i/3)$and$n$positive real numbers$ 0=\tau_0 < \tau_1 < \tau_2 < ...\tau_{n-1}< \tau_n=1 $such that ... 1answer 93 views Problem with making an estimate when values of many variables are unknown? Hi all, I was wondering whether you could help me understand a part in a proof that is assumed to be an "obvious detail" by the author, but that I can't wrap my head around. Essentially, as far as I ... 1answer 684 views On an eigenvalue inequality Let$\lambda_1 (\cdot)$be the larger absolute value eigenvalue of a$2\times2$matrix and$\lambda_2 (\cdot)$the smaller absolute value eigenvalue of a$2\times2$matrix, i.e.$|\lambda_1 (\cdot)| ...
Could somebody help me to answer the following question? Let $f:R_+ \rightarrow R_+$ be a nonindentically zero, nondecreasing, continuous, concave function with $f(0)=0$. Do we have that for any ...