Results 51 to 60 of about 553 (125)
Simultaneous approximation by neural network operators with applications to Voronovskaja formulas
Mathematische Nachrichten, Volume 298, Issue 3, Page 871-885, March 2025.Abstract 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 the sigmoidal function. Other than a uniform convergence theorem for the derivatives of NN operators, we also provide a quantitative estimate for the order of ...
Marco Cantarini, Danilo Costarelli
wiley +1 more source
Dunkl generalization of q-Szász-Mirakjan Kantorovich operators which preserve some test functions
Journal of Inequalities and Applications, 2016 In this paper we introduce q-Szász-Mirakjan-Kantorovich operators generated by a Dunkl generalization of the exponential function and we propose two different modifications of the q-Szász-Mirakjan-Kantorovich operators which preserve some test functions.
Mohammad Mursaleen +2 more
doaj +1 more source
Approximation by q-Szasz operators [PDF]
, 2010 his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given.
Mahmudov, Nazim I.
core
A Bernstein‐Like Trigonometric Basis: Properties, Curve Design, and Operator Construction
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.We introduce a novel family of trigonometric basis functions equipped with a shape parameter, analogous to Bernstein functions. These basis functions are employed to construct Bézier‐like curves, termed “trigo‐curves”, which retain the fundamental properties of classical Bézier curves while offering enhanced shape control through parameter adjustment ...
Jamshid Saeidian +3 more
wiley +1 more source
Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and xj
Mathematical Methods in the Applied Sciences, Volume 47, Issue 18, Page 13718-13733, December 2024.Recently, the authors constructed operators acting on a space of functions defined on [0,∞)$$ \left[0,\infty \right) $$ and preserving 1 and xj$$ {x}^j $$ for a given j∈ℕ$$ j\in \mathrm{\mathbb{N}} $$. To this end, they considered suitable modifications of the Post–Widder and gamma operators.
Ulrich Abel +3 more
wiley +1 more source
Parametric Extension of a Certain Family of Summation-Integral Type Operators
Cumhuriyet Science Journal, 2023 In this paper, we introduce a parametric extension of a certain family of summation-integral type operators on the interval [0,∞). Firstly, we obtain test functions and central moments. Secondly, we investigate weighted approximation properties for these
İsmet Yüksel, Nadire Fulda Odabaşı
doaj +1 more source
Stancu type q-Bernstein operators with shifted knots
Journal of Inequalities and Applications, 2020 In the present paper, Stancu type generalizations of the q-analog of Lupaş Bernstein operators with shifted knots are introduced. Some approximation results and rate of convergence for these operators are investigated.
M. Mursaleen +3 more
doaj +1 more source
Generalized p,q-Gamma-type operators
Journal of Function Spaces, 2020 In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of ...
Wen-Tao Cheng, Qing-Bo Cai
doaj +1 more source
The Lower Estimate for Bernstein Operator [PDF]
, 2013 MSC 2010: 41A10, 41A15, 41A25, 41A36For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of ...
Gal, Sorin G., Tachev, Gancho T.
core
A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators
Constructive Mathematical Analysis, 2019 In this note we establish a quantitative Voronovskaja theorem for modified Bernstein polynomials using the first order Ditzian-Totik modulus of smoothness.
openaire +3 more sources