q-Szász operators which preserve x 2

Abstract

ABSTRACT. In the present paper we construct q-Szász operators that preserve the third test function e 2 . Rate of global convergence is obtained in the frame of weighted spaces. Furthermore, we obtain a Voronovskaja type theorem for these operators. This sequence preserves the test functions e 0 , e 2 and V n (e 1 ; x) = r * n (x) holds. The goal of this article is to construct and investigate a variant of q-Szász-Mirakjan operators in the case q > 1, studied in [10], which preserve the functions e 0 and e 2 . Constructed operator has a better rate of convergence than the classical King type Szász-Mirakjan operators studied in [3].The paper is organized as follows. In Section 2, we give standard notations that will be used throughout the paper, introduce King type q-Szász operators and evaluate their moments. In Section 3, we study convergence properties of our operators for functions with polynomial growth. The main tool is a weighted modulus of smoothness. Furthemore we give a Voronovskaja-type asymptotic formula.

Bernstein approximations in glasso‐based estimation of biological networks

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Voronovskaja Type Approximation Theorem for q-Szasz–Schurer Operators

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