Displaying similar documents to “Generalized order and best approximation of entire function in L p -norm.”

On approximation and interpolation of entire functions with index-pair (p,q).

H. S. Kasana, Devendra Kumar (1994)

Publicacions Matemàtiques

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In this paper we have studied the Chebyshev and interpolation errors for functions in C(E), the normed algebra of analytic functions on a compact set E of positive transfinite diameter. The (p,q)-order and generalized (p,q)-type have been characterized in terms of these approximation errors. Finally, we have obtained a saturation theorem for f ∈ C(E) which can be extended to an entire function of (p,q)-order 0 or 1 and for entire functions of minimal generalized (p,q)-type.

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

Xiao-Min Li, Hong-Xun Yi (2009)

Czechoslovak Mathematical Journal

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We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.