Bounded variation and differentiability of functions.
Boundedness of classical operators on classical Lorentz spaces
Boundedness of fractional maximal operators between classical and weak-type Lorentz spaces [Book]
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces.
Boundedness properties for functional inequalities.
Boundedness properties of fractional integral operators associated to non-doubling measures
The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions for doubling...
Bounds for certain delay integral inequalities on time scales.
Bounds for certain new integral inequalities on time scales.
Bounds for Convex Functions of Čebyšev Functional Via Sonin's Identity with Applications
Some new bounds for the Čebyšev functional in terms of the Lebesgue norms and the -seminorms are established. Applications for mid-point and trapezoid inequalities are provided as well.
Bounds for entropy and divergence for distributions over a two-element set.
Bounds for -divergences under likelihood ratio constraints
In this paper we establish an upper and a lower bound for the -divergence of two discrete random variables under likelihood ratio constraints in terms of the Kullback-Leibler distance. Some particular cases for Hellinger and triangular discimination, -distance and Rényi’s divergences, etc. are also considered.
Bounds for quotients in rings of formal power series with growth constraints
In rings of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to , provided is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that...
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...
Bounds for some perturbed Čeby'ev functionals.
Bounds for the 3x+1 problem using difference inequalities
Bounds for the beta function
Bounds for the Čebyšev functional of a convex and a bounded function.
Bounds of the roots of the real polynomial
An algorithm for the calculation of a lower bound of the absolute values of the roots of a real algebraic polynomial, of an arbitrary degree, is derived. An example is given to compare the bounds calculated by the method proposed and by other methods.
Bounds on certain integral inequalities.
Bounds on the deviation of a function from its averages