Stancu‐type generalization of Dunkl analogue of Szász–Kantorovich operators

Abstract

The purpose of the paper is to introduce Stancu‐type linear positive operators generated by Dunkl generalization of exponential function. We present approximation properties with the help of well‐known Korovkin‐type theorem and weighted Korovkin‐type theorem and also acquire the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K‐functional, and second‐order modulus of continuity by Dunkl analogue of Szász operators. Copyright © 2015 John Wiley & Sons, Ltd.

Modified Stancu type Dunkl generalization of Szász–Kantorovich operators

“…We modify the Szász-Mirakjan-Kantrovich operators [5] and define a Dunkl generalization of these modified operators (or a modification of Dunkl generalization of Szász-Mirakjan-Kantrovich operators [9]) as follows:…”

“…For µ ≥ 0, x ≥ 0, and f ∈ C[0, ∞), Gürhan Içöz [9] gave a Dunkl generalization of Kantrovich type integral generalization of Szász operators as follows:…”

“…In [5,6,7], various better approximation properties of the Szász-Mirakjan-Kantrovich operators, Szász-Mirakjan operators and Szász-Mirakjan-Beta operators were investigated. Recently, in [5,9], by modifying the Dunkl generalization of Szász-Mirakjan operators, we have showed that our modified operators have better error estimation than the classical ones. In this paper, we apply the Dunkl generalization to the modified Szász-Mirakjan-Kantorovich operators [5] and a better approximation to Szász-Mirakjan-Stancu operators [9].…”

“…Recently, in [5,9], by modifying the Dunkl generalization of Szász-Mirakjan operators, we have showed that our modified operators have better error estimation than the classical ones. In this paper, we apply the Dunkl generalization to the modified Szász-Mirakjan-Kantorovich operators [5] and a better approximation to Szász-Mirakjan-Stancu operators [9].…”

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AbstractIn this paper, we introduce a modification of the Szász-Mirakjan-Kantorovich operators as well as Stancu operators [9] (or a Dunkl generalization of modified Szász-Mirakjan-Kantrovich operators [5]) which preserve the linear functions. These types of operators modification enables better error estimation on the interval [ 1 2 , ∞) than the classical Dunkl Szász-MirakjanKantrovich as well as Stancu operators.

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