Abstract
The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval [ frac{1}{2},infty ). This type of modification allows a better estimation of the error on [ frac{1}{2},infty ) rather than [ 0,infty ). We establish Korovkin type result in weighted spaces and also study approximation properties with the help of modulus of continuity of order one, Lipschitz type maximal functions, and Peetre’s K-functional. Furthermore, we estimate the degrees of approximations of the operators by modulus of continuity of order two.
Highlights
1 Introduction and preliminaries The first most elegant and easiest proof of Weierstrass approximation theorem was given by S.N Bernstein by introducing positive linear operators [8] known as Bernstein operators
The q-analogue of the Bernstein operators was studied by Lupaş [17] and Phillips [33]
Szász operators have been studied via Dunkl modification such as the classical Dunkl Szász operators [37], q-Dunkl–Szász operators [14], and (p, q)-Dunkl–Szász operators [7]
Summary
; for more details on [n]p,q-integers, see [16]. For the exponential function on (p, q)-analogues one has ep,q(x) =. The q-Hermite type polynomials on q-Dunkl were given in [10] and a recursion formula was obtained by applying a relation
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