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A Korovkin type approximation theorems via -convergence

Oktay Duman (2007)

Czechoslovak Mathematical Journal

Using the concept of -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

A note on one of the Bernstein theorems

Jiří Brabec (1993)

Mathematica Bohemica

One of the Bernstein theorems that the class of bounded functions of the exponential type is dense in the space of bounded and uniformly continuous functions. This theorem follows from a convergence theorem for some interpolating operators on the real axis.

A note on the convergence of partial Szász-Mirakyan type operators

Monika Herzog (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In this paper we study approximation properties of partial modified Szasz-Mirakyan operators for functions from exponential weight spaces. We present some direct theorems giving the degree of approximation for these operators. The considered version of Szász-Mirakyan operators is more useful from the computational point of view.

A remark on a modified Szász-Mirakjan operator

Guanzhen Zhou, Songping Zhou (1999)

Colloquium Mathematicae

We prove that, for a sequence of positive numbers δ(n), if n 1 / 2 δ ( n ) ¬ as n , to guarantee that the modified Szász-Mirakjan operators S n , δ ( f , x ) converge to f(x) at every point, f must be identically zero.

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