Authors:Jorge Bustamante, Abisaí Carrillo-Zentella, and José M. Quesada
We present direct and strong converse theorems for a general sequence of positive linear operators satisfying some functional equations. The results can be applied to some extensions of Baskakov and Szász–Mirakyan operators.
Recently P. Mache and M. W. Müller introduced the Baskakov quasi-interpolants and obtained an approximation equivalence theorem.
In this paper we consider simultaneous approximation equivalence theorem for Baskakov quasi-interpolants.
The uniform weighted approximation errors of Baskakov-type operators are characterized for weights of the form for γ0,γ∞∊[−1,0]. Direct and strong converse theorems are proved in terms of the weighted K-functional.
Authors:Borislav R. Draganov and Parvan E. Parvanov
Best trigonometric approximation in Lp, 1≦p≦∞, is characterized by a modulus of smoothness, which is equivalent to zero if the function is a trigonometric polynomial of a given degree. The characterization is similar to the one given by the classical modulus of smoothness. The modulus possesses properties similar to those of the classical one.