On Generalized Bernstein Polynomials
Copyright policy )On Generalized Bernstein Polynomials
The generalized Bernstein polynomials of Jakimovski and Leviatan and the generalized Euler summability method of Wood are considered in the general context of Gronwall-like transformations. It is shown under general circumstances that, for bounded sequences, generalized Euler summability is equivalent to Euler summability. A class of generalized Bernstein polynomials which are generated by certain Gronwall methods is defined and the members of this class which possess the uniform approximation property are characterized.
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Approximation by polynomials, Special methods of summability, Approximation by operators (in particular, by integral operators)
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Approximation by polynomials, Special methods of summability, Approximation by operators (in particular, by integral operators)
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