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.
On the rate of approximation in the random sum CLT for dependent variables
Capital and lower-case approximations of the expected value of a class of smooth functions of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).
On the rate of convergence for bivariate Beta operators.
On the rate of convergence for modified Szász-Mirakyan operators on functions of bounded variation.
On the rate of convergence of certain approximation operators.
On the rate of convergence of Hermite-Fejér polynomials to functions of bounded variation on the zeros of certain Jacobi polynomials