Approximation of growth numbers of generalized bi-axially symmetric potentials

• Autorzy: Kumar D.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-Axiaily Symmetric Potentials (GBASP's). The GBASP's are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The author has been obtained the characterizations of the (/-growth number and lower q-growth number of a GBASP &isin H R, O < R < &infin in terms of rate of decay of approximation error En(H, Ro}, 0 < Ro < &infin. Finally we have obtained a necessary condition for a GBASP &isin HR to be of perfectly regular growth.

Słowa kluczowe

EN

generalized biaxially symmetric potentials; index q; polynomial approximates in sup norm

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 51--60
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kumar D.

• Department of Mathematics, Faculty of Science, P.O. Box 1176 Addis Ababa University, Addis Ababa, Ethiopia,

Bibliografia

• [1] S.K. Bajpei, G.P. Kapoor, O.P. Juneja, On entire functions of fast Growth, Trans. Amer. Math. Soc., 203(1975), 275-298.
• [2] R.P. Gilbert, Intrigal operator methods in bi-axially symmetric potentials theory, Contrib. Diff. Eqns., 2(1963), 441-458.
• [3] O.P. Juneja, Some properties of entire functions. Dissertation, Indian Institute of Technology, Kanpur, 1965.
• [4] G.P. Kapoor, On the proximate order and maximum term of functions analytic in the unit disc, Rev Roumaine Math. Pures Appl., 18(1973), 1207-1215.
• [5] D. Kumar, H.S. Kasana, On approximation of generalized bi-axially symmetric potentials, Soochow J. Math., 21 (4)(1995), 365-375.
• [6] P.A. Mccoy, Approximation of pseudoanalytic functions on the disk, Complex Variables: Theory Appl. 6(1986), 123-133.
• [7] P. A. Mccoy, Polynomials approximation of generalized bi-axially symmetric potentials, J. Approx. Theory, 25(1979), 153-168.