Abstract
In the present paper, the Bezier variant of Jakimovski-Leviatan-Peltenea operators involving Sheffer polynomials is introduced and the degree of approximation by these operators is investigated with the aid of Ditzian-Totik modulus of smoothness, Lipschitz type space and for functions with derivatives of bounded variations.
Highlights
The Bézier variant of Jakimovski-LeviatanPa1⁄4lta1⁄4nea operators involving She¤er polynomials is introduced and the degree of approximation by these operators is investigated with the aid of DitzianTotik modulus of smoothness, Lipschitz type space and for functions with derivatives of bounded variations
Approximation theory is a crucial branch of Mathematical analysis
In 1950, Szasz [14] introduced a generalization of Bernstein polynomials on the in...nite interval [0; 1) and established the convergence properties of these operators
Summary
Approximation theory is a crucial branch of Mathematical analysis. The fundamental property of approximation theory is to approximate a function f by another functions which have better properties than f. Inspired by the work of Verma and Gupta [15], Mursaleen et al [9] de...ned the Jakimovski-Leviatan-Pa1⁄4lta1⁄4nea operators by means of She¤er polynomials, and integral modi...cation of the operators given by (0.6), as. 1 and established some convergence properties of these operators with the help of the Korovkin-type theorem, rate of convergence by using Ditzian-Totik modulus of smoothness and approximation properties for the functions having derivatives of bounded variation. Zeng [17] introduced the Szasz-Bézier operators and discussed the rate of convergence of these operators for the functions of bounded variations. The organization of the paper as follows: In Section 1, the Bézier variant of Jakimovski-Leviatan-Pa1⁄4lta1⁄4nea operators involving She¤er polynomials has been introduced.
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