Related papers: Global approximation theorems for general gamma ty…
We prove quantitative Runge type approximation results for spaces of smooth zero solutions of several classes of linear partial differential operators with constant coefficients. Among others, we establish such results for arbitrary…
In the present paper, we consider (p,q)-analogue of the Beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
We present a new neural network to approximate convex functions. This network has the particularity to approximate the function with cuts and can be easily adapted to partial convexity. We give an universal approximation theorem in the full…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In the present paper, we introduce a Choldowsky type generalization of the q Favard-Szasz operators and obtain weighted statistical approximation properties of these operators. We also establish the rates of statistical convergence by means…
A fast approximation to the Boys functions (related to the lower incomplete gamma function of half-integer parameter) by a single closed-form analytical expression for all argument values have been developed and tested. Besides the…
In this paper, we introduce the higher order generalization of Bernstein type operators defined by (p,q)-integers. We establish some approximation results for these new operators by using the modulus of continuity.
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$. Especially, for a given $G$-invariant/equivariant function, we construct its universal…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
In this paper, we are dealing with a new type of Baskakov-Schurer-Szasz operators (\ref{eq1}). Approximation properties of this operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the…
In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical…
The goal of this note is to consider Liouville type theorem for p-Laplacian type operators. In particular guided by the Laplacian case one establishes analogous results for the p-Laplacian and operators of this type.
In the present paper, we consider $(p,q)$-analogue of the Baskakov-Beta operators and using it, we estimate some direct results on approximation. Also, we represent the convergence of these operators graphically using MATLAB.
We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We introduce and study a family of integral operators in the Kantorovich sense for functions acting on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform…