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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.

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.