A generalized Dunkl type modifications of Phillips operators

Abstract

The main purpose of this present article is to discuss the convergence of Lebesgue measurable functions by providing a Dunkl generalization of Szász type operators known as Phillips operators. To achieve the results of a better way of uniform convergence of the Phillips operators, we study qualitative results in a Korovkin and weighted Korovkin space.

Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

“…Studies on Dunkl type generalizations [14] and previous studies of Szász type operators [6,7] demonstrate an error estimation to the operators which allow us much faster approximation to the function which is being approximated. In this paper, we modify the Phillips operators given by [14] via Dunkl generalization. Our main idea is to approximate these operators by well known Korovkin's and weighted Korovkin's theorems.…”

“…where 0 ≤ α ≤ β. Note that if we take α = β = 0 in (12), then the operators S * n,υ reduce to operators defined by (11) and if take χ n (x) = x in P n,υ , then we get the operators defined studied in [14].…”

Dunkl generalization of Phillips operators and approximation in weighted spaces

“…Studies on Dunkl type generalizations [13] and previous studies of Szász type operators [6,7] demonstrate an error estimation to the operators which allow us much faster approximation to the function which is being approximated. In this paper, we modify the Phillips operators given by [13] via Dunkl generalization. Our main idea is to approximate these operators by well known Korovkin's and weighted Korovkin's theorems.…”

“…Note that if we take α = β = 0 in (9), then the operators S * n,υ reduce to operators defined by (9) and if take χ n (x) = x in P n,υ , then we get the operators defined studied in [13].…”

Approximation on a class of Szász–Mirakyan operators via second kind of beta operators

“…Researchers have obtained several approximations of Szász-Mirakyan type operators via Dunkl generalization; for instance, see [6,18,26,28,29,32,39]. Related to these results, more approximation results have been studied in different functional spaces (see [1,2,4,5,14,38] and [3,16,27,31]).…”