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On q-Szász-Durrmeyer operators

Nazim Mahmudov, Havva Kaffaoğlu (2010)

Open Mathematics

In the present paper, we introduce the q-Szász-Durrmeyer operators and justify a local approximation result for continuous functions in terms of moduli of continuity. We also discuss a Voronovskaya type result for the q-Szász-Durrmeyer operators.

On regularization in superreflexive Banach spaces by infimal convolution formulas

Manuel Cepedello-Boiso (1998)

Studia Mathematica

We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex C 1 , α functions converging to f uniformly on bounded sets and...

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