26 Results Found

In this paper, we construct a new variant of the classical Szász–Mirakyan operators, $M_n$, which fixes the functions 1 and $e^{ax},x\ge 0,a\in \mathbb{R}$. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of $M_n$ and...

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 appr...

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation oper...

The aim of this paper is to consider bicomplex Favard–Szász–Mirakjan operators and study some approximation properties on a compact ${\mathbb{C}}_2$ disk. We provide quantitative estimates of the convergence. Moreover, the Voronovskaja-type resu...

The main purpose of this paper is to define a new family of Szász–Mirakyan operators that depends on a non-negative parameter, say $\alpha$. This new family of Szász–Mirakyan operators is crucial in that it includes both the...

This article is concerned with the Durrmeyer-type generalization of Szász operators, including confluent Appell polynomials and their approximation properties. Also, the rate of convergence of the confluent Durrmeyer operators is found by usin...

In this paper, we primarily use Stancu variants of Kantorovich-type operators to investigate the convergence and other associated properties of new Szász–Mirakjan operators. We compute the moments and central moments of the new Szá...

This research work focuses on $\lambda$-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in $\lambda$-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approxim...

In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences ${\alpha }_n$, ${\beta }_m$ and ${\xi }_m$ of positive numbers. Then, we obtain the rate of co...

In this paper, as a generalization of Szasz operators, a brand-new sequence of operators including the Appell polynomials of class $A^{\left(2\right)}$ is introduced. First, the convergence of this new sequence of operators is obtained, and then, some approximation re...

In this paper, we define the $(p,q)$ -variant of Szász–Kantorovich operators via Dunkl-type generalization generated by an exponential function and study the Korovkin-type results. We also obtain the convergence of our operators...

This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to di...

We examine a Szász–Mirakyan–Durrmeyer type operator that reproduces the functions 1 and $e^{2ax}$ for a fixed parameter $a>0.$ While its exponential reproduction property has been described in the classical literature, the effect of ex...

The goal of this manuscript is to introduce a new Stancu generalization of the modified Szász–Kantorovich operator connecting Riemann–Liouville fractional operators via Charlier polynomials. Further, some estimates are calculated as test functions an...

In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the es...

The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defin...

In this paper, we introduce a generalization of the Kantrovich–Stancu-type Szasz operator asymmetry with hybrid families of special polynomials. Additionally, we construct certain positive linear operators together with the Sheffer–Appell polynomial...

This paper is concerned with the adaptive backstepping synchronization control for a class of variable-order (VO) fractional uncertain nonlinear system with external disturbances and a dead zone. A kind of VO fractional command filter is employed to...

This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by t...

This paper is concerned with the sequence of positive linear operators obtained by certain generating functions of polynomials and with investigation of its approximation properties in detail. Initially, the convergence theorem is expressed for the s...

In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS for...

In this contribution, we define a new operator sequence which contains analytic functions. Using approximation techniques found by Korovkin, some results are derived. Moreover, a generalization of this operator sequence called Kantorovich type genera...

In the present paper, we give an operator with the help of a generalization of Boas–Buck type polynomials by means of Gamma function. We have approximation properties and moments. The rate of convergence is given by the Ditzian–Totik first order modu...

This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various funct...

The B$\acute{e}$zier-type operator has become a powerful tool in operator theory, neural networks, curve and surface design and representation because of its good shape-preserving properties. Motivated by the improvements of the operator in computationa...

This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence a...