Weighted and Voronovskaja type approximation by q-Sz´ asz-Kantorovich operators involving Appell polynomials
Abstract
In this article, we concentrate on the Szász-Jakimovski-Leviatan operators imposed by
Appell polynomials using q-calculus. We analyze the classical Szász-Jakimovski-Leviatan-
Kantorovich and derive the approximation results connected to the non-negative parameters
ς ∈ [ 1/2 ,∞) in q-analogue. In order to combining with the earlier investigation by utilizing the
Korovkin’s theorem we study the local as well as global approximation theorems in terms of
uniform modulus of continuity of order one and two. We calculate the rate of convergence by
using of Lipschitz-maximal functions. Moreover, the Voronovskaja-type approximation theorem
is also calculated here.
Appell polynomials using q-calculus. We analyze the classical Szász-Jakimovski-Leviatan-
Kantorovich and derive the approximation results connected to the non-negative parameters
ς ∈ [ 1/2 ,∞) in q-analogue. In order to combining with the earlier investigation by utilizing the
Korovkin’s theorem we study the local as well as global approximation theorems in terms of
uniform modulus of continuity of order one and two. We calculate the rate of convergence by
using of Lipschitz-maximal functions. Moreover, the Voronovskaja-type approximation theorem
is also calculated here.
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