Approximation theorems for Markov operators

Direct Approximation Theorems for Discrete Type Operators

In the present paper we prove direct approximation theorems for discrete type operators (Lnf)(x) = ∞ ∑ k=0 un,k(x)λn,k(f), f ∈ C[0,∞), x ∈ [0,∞) using a modified K−functional. As applications we give direct theorems for Baskakov type operators, Szász-Mirakjan type operators and Lupaş operator.

Approximation Theorems for Generalized Complex Kantorovich-Type Operators

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials q > 0 attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∈ C : |z| < R}, R > q, the rate of approximation by the q-Kantorovich operators q > 1 is of order q−n versus 1/n for the classical K...

Ovidiu T . Pop VORONOVSKAJA - TYPE THEOREMS AND APPROXIMATION THEOREMS FOR A CLASS OF GBS OPERATORS

In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through particular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, BleimannButzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.

Korovkin-type Theorems and Approximation by Positive Linear Operators

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L-functions, by means of positive linear operators. The paper also contains several new results and applications. Moreover, the organization of the subject follows a simple and direct approach which quick...

Inverse Approximation Theorems for . . .