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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 new approach to nonlinear singular integral operators depending on three parameters

Gumrah Uysal (2016)

Open Mathematics

In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , T λ ( f ; x , y ) = 2 ( t - x , s - y , f ( t , s ) ) d s d t , ( x , y ) 2 , λ Λ , where Λ is a set of non-negative numbers with accumulation point λ0.

A New Characterization of Weighted Peetre K-Functionals (II)

Draganov, Borislav, Ivanov, Kamen (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented...

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