Vol. 40, No. 1, 1972

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On polynomials approximating the solutions of nonlinear differential equations

Alex Bacopoulos and Athanassios G. Kartsatos

Vol. 40 (1972), No. 1, 1–5
Abstract

Suppose that L(x) is a differential operator and R(t) a continuous function, and consider the differential equation () L(αj) = R(t). Then a problem in approximation theory is whether we can approximate a solution x(t) of () uniformly with a sequence of polynomials Pn for which we have R(t) L(Pn)ηn, where ∥⋅∥ is a certain norm and ηn a specific sequence of nonnegative constants. This is done here for a first order nonlinear differential operator L and for two different norms, the uniform norm and the Lp norm (1 p < +).

Mathematical Subject Classification 2000
Primary: 34A45
Secondary: 41A10
Milestones
Received: 16 September 1970
Revised: 10 November 1970
Published: 1 January 1972
Authors
Alex Bacopoulos
Athanassios G. Kartsatos