On Szász-Durrmeyer type modification using Gould Hopper polynomials

Abstract

<p style='text-indent:20px;'>In the present article, we study a generalization of Szász operators by Gould-Hopper polynomials. First, we obtain an estimate of error of the rate of convergence by these operators in terms of first order and second order moduli of continuity. Then, we derive a Voronovkaya-type theorem for these operators. Lastly, we derive Grüss-Voronovskaya type approximation theorem and Grüss-Voronovskaya type asymptotic result in quantitative form.</p>

A generalization of szász operators with the help of new kind Appell polynomials

“…Gould Hopper polynomials are the Appell polynomials of class A (2) by choosing where x ∈ [0, ∞). And also many authors today have included approximation and Gould Hopper polynomials in their current articles [22], [16].…”

Double Sums of the Szasz Sequence

“…In 1969, Jakimovski and Leviatan modified the Sazsz sequence using the Apple polynomials called the Szasz-Jakimovski-Leviatan sequence [2].In 1974, the Szasz-Jakimovski-Leviatan sequence is generalized by using Sheffer polynomials [3]. In 1988, to establish a summation-integral type on the space of integrable functions on [0, ∞) suggest a series of modified Sazsz operators [4]. In 1994-1997, Ciup provides and establishes a few approximation properties for the operators (1); for additional information, see [5][6].…”

Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators

“…For the more information about the Durrmeyer operators and their properties, readers should refer the following articles (cf. [5,29,23,25,36,31,9,32,28]).…”