On the Minimum Norm Projection on Closed Subspaces of L^p[0, 2*pi] and an Application
On the monotonicity of sequences of quadrature formulae.
On the multivariate transfinite diameter
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
On the nonexistence of some interpolatory polynomials.
On the Number of Best Approximation in Certain Non-linear Families of Functions.
On the Number of Best Approximations in Certain Non-Linear Families of Functions. (Short Communication).
On the Number of Zeros of Functions in a Weak Tchebyshev-Space.
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the operator of Bleimann, Butzer and Hahn.
On the order of approximation of functions by the bidimensional operators Favard-Szász-Mirakyan.
On the points of multivaluedness of metric projections in separable Banach spaces
On the points of multivaluedness of monotone operators
On the positivity of certain Cotes numbers.
On the positivity of ultraspherical type quadrature formulas with Jacobi abscissas.
On the power-series expansion of a rational function
Introduction. The problem of determining the formula for , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part of the solution...
On the projection norm for a weighted interpolation using Chebyshev polynomials of the second kind.
On the proof of Erdős' inequality
Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality for a constrained polynomial of degree at most , initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval and establish a new asymptotically sharp inequality.
On the quantitative Fatou property
The result of this article together with [1] and [4] gives a full quantitative description of a Fatou type property for functions from Hardy classes in the upper half plane.
On the randomized complexity of Banach space valued integration
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by if and only if X is of equal norm type p.
On the rate of approximation for the Bézier variant of Kantorovich-Balazs operators.