Related papers: A note on comparison between Birkhoff and McShane-…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…
We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold $M$. Applications are given to the Hausdorff measure of the intersection of the variety with $M$…
In the present note we prove a multiplicity result for a Kirchhoff type problem involving a critical term, giving a partial positive answer to a problem raised by Ricceri.
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We introduce the forward (backward) gH-difference operator of interval sequences, and establish some new discrete Opial type inequalities for interval-valued functions. Further, we obtain generalizations of classical discrete Opial type…
In this manuscript, the author derived a definite integral involving the logarithmic function, function of powers and polynomials in terms of the Lerch function. A summary of the results is produced in the form of a table of definite…
The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
We build bounded solutions to a linear integral equation. Our functions are built as limit of iterated Birkhoff sums over auto-similar dynamical systems. Nous construisons des solutions born\'ees \`a une \'equation int\'egrale. Notre…
Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
This survey discusses the classical Bernstein and Markov inequalities for the derivatives of polynomials, as well as some of their extensions to general sets.
An Ostrowski type integral inequality for convex functions and applications for quadrature rules and integral means are given. A refinement and a counterpart result for Hermite-Hadamard inequalities are obtained and some inequalities for…
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…
Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.
We prove a binomial formula for Macdonald polynomials and consider applications of it.
We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…
We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to the problem.
We give a simple proof of a functional version of the Blaschke-Santalo inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke-Santalo inequality.