We give estimates for the approximation numbers of composition operators on H, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by e−c √ . When the symbol is continuous on the closed unit disk and has a domain touching the boundary non-tangentially at a finite number of points, with a good behavior a...

Abstract In this paper, a new approach to the numerical solution of VolterraFredholm integral equations by using expansion method based on the composition of the inverse and direct discrete fuzzy transforms (shortly F-transforms) in combination with the collocation technique is proposed. First, the unknown function is approximated by using the composition of the inverse and direct discrete F-tr...

In this study, we define a Kantorovich type generalization of W. MeyerKönig and K. Zeller operators and we will give the approximation properties of these operators with the help of Korovkin theorems. Then we compute the approximation order by modulus of continuity.

*Correspondence: [email protected] 4School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, China Full list of author information is available at the end of the article Abstract In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of (p,q)-integers. We obtain moments and centr...

The aim of this paper is to present a Stancu type Kantorovich modification of q−BernsteinSchurer operators introduced by Muraru [22] and modified by Ren and Zeng [29]. Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we estab...

In this paper we introduce the Bézier variant of genuine-Durrmeyer type operators having Pólya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for funct...

Let N be a set of positive integers and let F(z) = I Anz" be an entire function for which An0 (n 0 N). It is reasonable to expect that, if D denotes the density of the set N in some sense, then F(z) will behave somewhat similarly in every angle of opening greater than 2vD. For functions of finite order, the appropriate density seems to be the P6lya maximum density 9. In this paper we introduce ...

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variati01~al analysis and its applications, especially for issues related to variational stability and optimizatiou. \Ve develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative ...

A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in [11]. Several results of the theory recall the classical complex analysis, whereas other results reflect the peculiarity of the quaternionic structure. The recent [1] identified a larger class of domains, on which the study of regular functions is most natural and not limited to t...