On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation

• Autorzy: Kumar Devendra , Alghamdi Azza M.

Identyfikatory

DOI

10.1515/dema-2022-0030

• Języki publikacji: EN

Abstrakty

EN

For an entire function solution of generalized bi-axisymmetric potential equation, we obtain a relationship between the generalized growth characteristics and polynomial approximation errors in sup norm by using the general functions introduced by Seremeta [On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. 88 (1970), no. 2, 291–301].

Słowa kluczowe

EN

entire GBSPs functions; GBSPs polynomial approximation error; generalized order; generalized type; Jacobi polynomials; Jacobi sup norm

PL

funkcja całkowita; błąd aproksymacji wielomianowej; wielomiany Jacobiego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 429--436
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kumar Devendra

• Department of Mathematics, Faculty of Sciences Al-Baha University, P.O. Box-7738, Alaqiq, Al-Baha-65799, Saudi Arabia
• Department of Mathematics, M.M.H. College, Ghaziabad-201001, U.P., India

autor

Alghamdi Azza M.

• Department of Mathematics, Faculty of Sciences Al-Baha University, P.O. Box-7738, Alaqiq, Al-Baha-65799, Saudi Arabia

Bibliografia

• [1] R. P. Gilbert, Integral operator methods in bi-axially symmetric potential theory, Contrib. Differ. Equ. 2 (1963), 441–456.
• [2] R. B. Kelman, Axisymmetric potential problems suggested by bilogical considerations, Bull. Amer. Math. Soc. 69 (1963), no. 6, 835–838.
• [3] P. A. McCoy, Polynomial approximation of generalized biaxisymmetric potentials, J. Approx. Theory 25 (1979), no. 2, 153–168.
• [4] P. A. McCoy, Approximation of pseudoanalytic functions on the unit disc, Complex Var. Elliptic Equ. 6 (1986), 123–133.
• [5] P. A. McCoy, Optimal approximation and growth of solutions to a class of elliptic partial differential differential equations, J. Math. Anal. Appl. 154 (1991), 203–211.
• [6] H. S. Kasana and D. Kumar, The L p-approximation of generalized bi-axially symmetric potentials, Int. J. Diff. Eqs. Appl. 9 (2004), no. 2, 127–142.
• [7] H. S. Kasana and D. Kumar, L p-approximation of generalized bi-axially symmetric potentials over Carathéodory domains, Math. Slovaca 55 (2005), no. 5, 563–572.
• [8] D. Kumar, Ultra-spherical expansions of generalized bi-axially symmetric potentials and pseudoanalytic functions, Complex Var. Elliptic Equ. 53 (2008), no. 1, 53–64.
• [9] D. Kumar, On the (p q, )-growth of entire function solutions of Helmholtz equation, J. Nonlinear Sci. Appl. 4 (2011), no. 1, 5–14.
• [10] D. Kumar, Growth and approximation of solutions to a class of certain linear partial differential equations in N, Math. Slovaca 64 (2014), no. 1, 139–154.
• [11] G. S. Srivastava, On the growth and polynomial approximation of generalized biaxisymmetric potentials, Soochow J. Math. 23 (1997), no. 4, 347–358.
• [12] M. N. Seremeta, On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. 88 (1970), no. 2, 291–301.
• [13] G. Szegö, Orthogonal Polynomials, Vol. 23, Colloquium Publications, American Mathematical Society, Providence, R.I. 1967.
• [14] A. J. Fryant, Growth and complete sequences of generalized bi-axially symmetric potentials, J. Differ. Equ. 31 (1979), 155–164.
• [15] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publisher Co., New York, 1949.
• [16] S. M. Shah, Polynomial approximation of an entire function and generalized orders, J. Approx. Theory 19 (1977), no. 4, 315–324.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).