Approximation by Szasz-Mirakjan-Baskakov operators based on shape parameter

In this work, we obtain the approximation properties of a new generalization of Szász-Mirakjan operators based on postquantum calculus.Firstly, for these operators, a recurrence formulation for the moments is obtained, and up to the fourth degree, the central moments are examined.Then, a local approximation result is attained.Furthermore, the degree of approximation in respect of the modulus of continuity on a finite closed set and the class of Lipschitz are computed.Next, the weighted uniform approximation on an unbounded interval is showed, and by the modulus of continuity, the order of convergence is estimated.Lastly, we proved the Voronovskaya type theorem and gave some illustrations to compare the related operators' convergence to a certain function.

In the present work a Jain type modification of the generalized Szász-Mirakyan operators that preserve constant and exponential mappings is presented. The introduction of this operator helps to extend the class of operators that preserve exponential functions. A particular expansion involving the Lambert W-function is established which is used to obtain properties of the operator. Moments, and central moments, are presented with some limiting properties. A Voronovskaya type theorem, as well as other theorems, are discussed with results. Other select properties are also presented.Moments, recurrence formulas, and other identities are established for these operators. Approximation properties are also obtained with use of the Bohman-Korovkin theorem.

Determination of statistical fluctuations in the ionization yield of low energetic electrons in hydrogen

Higher order analytical nodal methods in response-matrix formulation for the multigroup neutron diffusion equations

Generalization of Szasz operators involving Brenke type polynomials

In this chapter, we consider the original space mapping (SM) to get a better comprehension of the technique. It concentrates on combative space mapping and its applications in antenna design. Antenna Theory: Analysis and Design, by Constantine A. Balanisoffers a uniquely balanced analysis of antenna fundamentals and microstrip antennas. Eliminating redundancy, it provides a theoretical background, application materials and details of recent progress. Exploring several effective design approaches, this chapter covers a wide scope and makes it an ideal hands-on resource for professionals seeking a refresher in the fundamentals. Our primary pivot in this chapter is to introduce some specific techniques that enable users to make optimal use of strong mercantile software packages and computational electromagnetics used in full-wave analysis and antenna design. Beyond specific numerical computations for wide concepts, this chapter systematically presents the all-important approximation methods using Taylor’s expansion and approach to analyzing microstrip structures including antennas. In this chapter, we consider the operator theory and Stancu-type generalization on considered summation integral operators for a function f(x) ∈ C ∞ [0, ∞), where x ∈ [0, ∞). On the other hand, we use hypergeometric series to obtain central moments for the operators. In the main results, we obtain asymptotic formula and some error estimates with a modulus of continuity.

In the present paper, we introduce the genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate the moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. We also calculate the second order central moment Znq,α((t−x)2;x). We give a Korovkin-type theorem; we estimate the rate of convergence for continuous functions. Furthermore, we prove a local approximation theorem in terms of second modulus of continuity; we obtain a local direct estimate for the genuine q-Stancu-Bernstein–Durrmeyer operators in terms of Lipschitz-type maximal function of order β and we prove a direct global approximation theorem by using the Ditzian-Totik modulus of second order.

In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin?s theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance v. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance v, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.

This paper is interested in a new sequence of linear positive operators including degenerate Appell polynomials. We give a convergence theorem for these operators and obtain the quantitative estimation of the approximation by using modulus of continuity, Peetre’s 𝒦-functional, Lipschitz class functions and a Voronovskaja-type theorem. In addition, we give a Kantorovich modification of these operators and derive some approximation properties.

<p style='text-indent:20px;'>The motive of this research article is to introduce a sequence of Sz<inline-formula><tex-math id="M2">\begin{document}$ \acute{a}sz $\end{document}</tex-math></inline-formula> Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in B<inline-formula><tex-math id="M3">\begin{document}$ \ddot{o} $\end{document}</tex-math></inline-formula>gel space via mixed modulus of continuity.</p>

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.

In this article, for the first time, the univariate symmetrized and perturbed hyperbolic tangent activated convolution-type operators of three kinds are introduced. Their approximation properties are presented, i.e., the quantitative convergence to the unit operator via the modulus of continuity. It follows the global smoothness preservation of these operators. The related iterated approximation as well as the simultaneous approximation and their combinations, are also extensively presented. Including differentiability and fractional differentiability into our research produced higher rates of approximation. Simultaneous global smoothness preservation is also examined.

In this paper, we have construct a new version of the Bézier‐type Baskakov–Schurer–Szász–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin‐type theorem, Voronovskaya‐type theorem, and Grüss–Voronovskaya‐type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz‐type space using the modulus of continuity and smoothness.

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

Numerical solution of stochastic differential equations by second order Runge–Kutta methods