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Approximation properties of certain summation integral type operators

Patel P., Mishra V. N.

Demonstratio Mathematica

2015

Vol. 48, nr 1

77--90

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

Asymptotics of the discrete spectrum for complex Jacobi matrices

Malejki M.

Opuscula Mathematica

2014

Vol. 34, no. 1

139--160

The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of infinite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in l2(N).

One can hear the area of a torus by hearing the eigenvalues of the polyharmonic operators

Guo S., Jin J.

Demonstratio Mathematica

2014

Vol. 47, nr 3

607--614

This paper considers the asymptotic properties for the spectrum of a positive integer power l of the Laplace–Beltrami operator acting on an n-dimensional torus T. If N(λ) is the number of eigenvalues counted with multiplicity, smaller than a real positive number λ, we establish a Weyl-type asymptotic formula for the spectral problem of the polyharmonic operators on T, that is, as (…), where (…) is the volume of the unit ball in Rn and Vol T is the area of T, which gives the information of the area of the torus based on the spectrum of the polyharmonic operators.

Unified elliptic-type integrals and asymptotic formulas

Chaurasia V., Pandey S.

Demonstratio Mathematica

2008

Vol. 41, nr 3

531-541

The object of the present paper is to consider a unified and extended form of certain families of elliptic-type integrals, which have been discussed in number of earlier works on the subject due to their importance and applications in problems arising in radiation physics and nuclear technology. The results obtained are of general character and include the investigations carried out by several authors. We obtain asymptotic formulas for the unified elliptic-type integrals.

On the rate of approximation of absolutely continuous functions by certain Kantorovich-type operators

Pych-Taberska P.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

193-202

The aim of this paper is to present estimates for the rate of pointwise convergence of the kantorovichians of the discrete Feller operators in some classes of absolutely continuous functions, in particular, for functions with derivatives of bounded variation in the generalized sense.