Results 81 to 90 of about 478 (139)

Approximation by some combinations of Poisson integrals for Hermite and Laguerre expansions

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2013
The aim of this paper is the study of a rate of convergence of some combinations of Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over the Poisson integrals.
Grażyna Krech, Eugeniusz Wachnicki
doaj  

Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval

Journal of Approximation Theory, 2014
In this paper, the authors have considered geometric series related to a large class of positive linear operators acting on a space of functions on the interval \([0, 1]\) and studied the convergence of the series in the case of sequences of admissible operators.
Abel, Ulrich, Ivan, Mircea, Păltănea, Radu   +2 more
openaire   +1 more source

On the Rate of Convergence and the Voronovskaya Theorem for the Poisson Integrals for Hermite and Laguerre Expansions

Journal of Approximation Theory, 2002
Let \(L^{(\alpha)}_n\) denote the \(n\)th Laguerre polynomial with parameter \(\alpha> -1\). The authors study properties of the Poisson integral \(A(f)\) defined for \(p\geq 1\) and \(f\in L^p([0,\infty), \omega_\alpha)\) by \[ A(f)(r, x):= \int^\infty_0 K_\alpha(r, x,y) f(y) \omega_\alpha(y) dy\qquad (0< \tau< 1, x> 0), \] where \(\omega_\alpha(y)= y^
Toczek, Grażyna, Wachnicki, Eugeniusz
openaire   +2 more sources

Quadrature rules associated with Baskakov quasi-interpolants

, 2014
Quadrature rules on the positive real half-line obtained by integrating the Baskakov quasi-interpolants described in \cite{MM, Sab7} are constructed and their asymptotic convergence orders are studied.
Sablonnière, Paul
core   +1 more source

Approximation by the new modification of Bernstein-Stancu operators

Cumhuriyet Science Journal, 2021
The current paper deals with the new modification of Bernstein-Stancu operators which preserve constant and Korovkin’s other test functions in limit case. We study the uniform convergence of the newly defined operators.
Melek Sofyalıoğlu, Kadir Kanat
doaj  

Approximation by a new Stancu variant of generalized (λ,μ)-Bernstein operators

Alexandria Engineering Journal
The primary objective of this work is to explore various approximation properties of Stancu variant generalized (λ,μ)-Bernstein operators. Various moment estimates are analyzed, and several aspects of local direct approximation theorems are investigated.
Qing-Bo Cai, Reşat Aslan, Faruk Özger, Hari Mohan Srivastava   +3 more
doaj   +1 more source

On the generalized Mellin integral operators

Demonstratio Mathematica
In this study, we give a modification of Mellin convolution-type operators. In this way, we obtain the rate of convergence with the modulus of the continuity of the mmth-order Mellin derivative of function ff, but without the derivative of the operator ...
Topuz Cem, Ozsarac Firat, Aral Ali
doaj   +1 more source

Approximation properties of modified Stancu beta operators

Journal of Numerical Analysis and Approximation Theory, 2006
In this paper we give approximation theorems for modified Stancu beta operators of differentiable functions. The Stancu beta operators were examined in [8, 1, 2, 5] and other papers.
L. Rempulska, M. Skorupka
doaj   +2 more sources

Approximation Properties of Baskakov-Balazs Type Operators for Functions of Two Variables [PDF]

, 2015
Atakut, Cigdem, Buyukyazici, Ibrahim, Kirci Serenbay, Sevilay   +2 more
core   +1 more source

Symmetrized Neural Network Operators in Fractional Calculus: Caputo Derivatives, Asymptotic Analysis, and the Voronovskaya–Santos–Sales Theorem

Axioms
This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of ...
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales, Gislan Silveira Santos   +2 more
openaire   +2 more sources