Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter δ_0

Abstract

In this paper, we define a new sequence of linear positive operators of integral type to approximate functions in the space,. First, we study the basic convergence theorem in simultaneous approximation and then study Voronovskaja-type asymptotic formula. Then, we estimate an error occurs by this approximation in the terms of the modulus of continuity. Next, we give numerical examples to approximate three test functions in the space by the sequence. Finally, we compare the results with the classical sequence of Szãsz operators on the interval . It turns out that, the sequence gives better than the results of the sequence for the two test functions using in the numerical examples.

Double Sums of the Szasz Sequence

“…In 2020, the Szasz sequence is generalized using a multiple of Sheffer polynomials [7]. For more details see [8][9][10][11]. For a function ℎ ∈ 𝐶 𝛼 [0, ∞) ≔ { ℎ ∈ 𝐶[0, ∞); |ℎ(𝑡)| ≤ 𝑀𝑒 𝛼𝑡 for some 𝛼 > 0} and 𝑠 ≥ − .…”

Simultaneous Approximation by a New Sequence of Integral Type Based on Two Parameters

“…After that, Mohammad and Abbod [8] introduced a general form for a sequence of positive and linear operators based on four parameters. Also, Mohammad and Muslim [9] studied the simultaneous approximation of a new sequence of integral type operators with parameter . Recently, in 2019, Mohammad and Hassan defined and studied a new sequence of positive and linear operators of integral type [10], as follows:…”