Abstract
The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.
Highlights
In the year 1950, a famous mathematician Szász [1] invented the positive linear operators for the continuous function f on 1⁄20, ∞Þ and that were extensively searched rather than Bernstein operators [2]
Where C1⁄20, ∞Þ is the space of continuous functions on 1⁄20, ∞Þ
Szász-Mirakjan operators were introduced by Sucu [3] by proposing an exponential function on Dunkl generalization by including a nonnegative number η ≥ 0, such that
Summary
In the year 1950, a famous mathematician Szász [1] invented the positive linear operators for the continuous function f on 1⁄20, ∞Þ and that were extensively searched rather than Bernstein operators [2]. For z ∈ 1⁄20,∞Þ and f ∈ C1⁄20,∞Þ, Szász introduced the operators as follows: Srð f ; zÞ = e−rz ∞ 〠 k=0 ðrzÞk k!. F kr, ð1Þ where C1⁄20, ∞Þ is the space of continuous functions on 1⁄20, ∞Þ. Szász-Mirakjan operators were introduced by Sucu [3] by proposing an exponential function on Dunkl generalization by including a nonnegative number η ≥ 0, such that S∗r ð f zÞ = 1 eηðrzÞ κ=0
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