On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

The Lower Estimate for Bernstein Operator

MSC 2010: 41A10, 41A15, 41A25, 41A36

Best Approximation and Moduli of Smoothness

2010 Mathematics Subject Classification: 41A25, 41A10.

A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.

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

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

On an Extremal Problem concerning Bernstein Operators

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.

Equivalence Between K-functionals Based on Continuous Linear Transforms

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.

Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

On the Convergence of (0,1,2) Interpolation

2000 Mathematics Subject Classification: 41A05.

Well-Posedness and Conditioning of Optimization Problems

AMS subject classification: 49K40, 90C31.

Approximation Properties of Schurer-Stancu Type Polynomials

MSC 2010: 41A25, 41A35

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

Approximation Classes for Adaptive Methods

* This work has been supported by the Office of Naval Research Contract Nr. N0014-91-J1343, the Army Research Office Contract Nr. DAAD 19-02-1-0028, the National Science Foundation grants DMS-0221642 and DMS-0200665, the Deutsche Forschungsgemeinschaft grant SFB 401, the IHP Network “Breaking Complexity” funded by the European Commission and the Alexan- der von Humboldt Foundation.

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10