## Functiones et Approximatio Commentarii Mathematici

### Approximation and generalized growth of solutions to a class of elliptic partial differential equations

#### Abstract

In the present paper, we study the approximation and growth of solutions to a class of elliptic partial differential equations. The characterizations of generalized order and generalized type of solutions to a class of elliptic partial differential equations have been obtained in terms of approximation errors.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 54, Number 1 (2016), 95-113.

Dates
First available in Project Euclid: 22 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.facm/1458656165

Digital Object Identifier
doi:10.7169/facm/2016.54.1.8

Mathematical Reviews number (MathSciNet)
MR3477737

Zentralblatt MATH identifier
06862337

#### Citation

Kumar, Susheel; Srivastava, Girja S. Approximation and generalized growth of solutions to a class of elliptic partial differential equations. Funct. Approx. Comment. Math. 54 (2016), no. 1, 95--113. doi:10.7169/facm/2016.54.1.8. https://projecteuclid.org/euclid.facm/1458656165

#### References

• S. Bergman, Integral operators in the theory of linear partial differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 23, Springer-Verlag, New York, 1969.
• A. Janik, On approximation of analytic functions and generalized order, Ann. Polon. Math. 55 (1991), 163–167.
• D. Kumar, Growth and Chebyshev approximation of entire function solutions of Helmoltz equation in ${\mathbb R}^{2}$, Eur. J. Pure Appl. Math. 3 (2010), no. 6, 1062–1069.
• P.A. McCoy, Optimal approximation and growth of solutions to a class of elliptic partial differential equations, J. Math. Anal. Appl. 154 (1991), 203–211.
• P.A. McCoy, Solutions of the Helmoltz equation having rapid growth, Complex Var. Elliptic Equ. 18 (1992), no. 1, 91–101.
• M.N. Seremeta, On the connection between the growth of a function analytic in a disc and moduli of the coefficients of its Taylor series, Visnik L'viv. Derzh. Univ. Ser. Mekh. Mat. 2 (1965), 101–110.
• G.S. Srivastava and S. Kumar, Generalized growth of solutions to a class of elliptic partial differential equations, Acta Math. Vietnam. 37 (2012), no. 1, 11–21.