A curious property of series involving terms of generalized sequences.
A new look at Newton's inequalities.
A new part-metric-related inequality chain and an application.
A note on a paper of H. Alzer and S. Koumandos.
A part-metric-related inequality chain and application to the stability analysis of difference equation.
A polynomial inequality generalising an integer inequality.
A sequence of sharp trigonometric inequalities
A sharp bound for a sine polynomial
We prove that for all integers n ≥ 1 and real numbers x. The upper bound Si(π) is best possible. This result refines inequalities due to Fejér (1910) and Lenz (1951).
A survey of recent reverses for the generalised triangle inequality in inner product spaces
A variance analog of majorization and some associated inequalities.
An equivalent form of the fundamental triangle inequality and its applications.
An inequality for polynomials with elliptic majorant.
An inequality for the coefficients of a cosine polynomial
We prove: If then The constant is the best possible.
An observation on the Turán-Nazarov inequality
The main observation of this note is that the Lebesgue measure μ in the Turán-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant ω ≥ μ, which can be effectively estimated in terms of the metric entropy of a set, and may be nonzero for discrete and even finite sets. While the frequencies (the imaginary parts of the exponents) do not enter the original Turán-Nazarov inequality, they necessarily enter the definition of ω.
Another refinement of Bernstein's inequality.
Asymptotic behavior for the best lower bound of Jensen's functional
Asymptotic expansion of the equipoise curve of a polynomial inequality.
Bernstein's inequality on algebraic curves
Bounds for entropy and divergence for distributions over a two-element set.
Bounds for sine and cosine via eigenvalue estimation
Define n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the first super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the first super- and subdiagonal are minus one. Then, denoting by λ(·) the largest eigenvalue, [...] Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain...