Related papers: Simultaneous approximation of translation operator…

It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…

We prove the existence of common hypercyclic, entire functions for certain families of translation operators.

We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.

We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…

We prove the existence of common hypercyclic entire functions for uncountable families of translation type operators. Contrary to our previous work [34], here the parameter which reflects the uncountable family lies on the unit circle. On…

We prove simultaneous Universal Approximation of a certain type of Pade Approximants and of Taylor series with the same indexes. This is a generic phenomenon in the space of holomorphic functions in any simply connected domain, as well as…

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

In this paper, we obtained some global approximation results for general Gamma type operators.

The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.

We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.

In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint…

A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.

In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…

In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of…

We show that families of translation operators, where the translates grow exponentially fast, do not admit common hypercyclic functions. The result is close to be optimal.

Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for…

In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of…