We construct the linear positive operators generated by the q-Dunkl generalization of the exponential function. We have approximation properties of the operators via a universal Korovkin-type theorem and a weighted Korovkin-type theorem. The rate of convergence of the operators for functions belonging to the Lipschitz class is presented. We obtain the rate of convergence by means of the classical, second order, and weighted modulus of continuity, respectively, as well.
This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.
In this work, the problem of the approximation by certain polynomials is addressed. A new type operators sequence including generalized Appell polynomials are defined, qualitative and quantitative approximation theorems are proved. Some explicit examples of our operators involving Hermite polynomials of ν variance, Gould-Hopper polynomials and Miller-Lee polynomials are given. Also, we present some numerical examples to confirm our theoretical results.
Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation and other associated properties of a class of the Szász-Mirakjan-type operators, which are introduced here by using an extension of the familiar Beta function. We propose to establish moments of these extended Szász-Mirakjan Beta-type operators and estimate various convergence results with the help of the second modulus of smoothness and the classical modulus of continuity. We also investigate convergence via functions which belong to the Lipschitz class. Finally, we prove a Voronovskaja-type approximation theorem for the extended Szász-Mirakjan Beta-type operators.
The aim of the paper is to introduce a Kantorovich-Stancu type modification of a generalization of Szász operators defined via Boas-Buck type polynomials and obtain rates of convergence for these operators. Furthermore, we give the figures for comparing approximation properties of the operators Kn and Bn.
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