scholarly journals Strong estimates of the weighted simultaneous approximation by the Bernstein and Kantorovich operators and their iterated Boolean sums

2015 ◽  
Vol 200 ◽  
pp. 92-135 ◽  
Author(s):  
Borislav R. Draganov
Keyword(s):  
Simultaneous Approximation ◽  
Boolean Sums ◽  
Kantorovich Operators

scholarly journals Approximation of Finite Hilbert and Hadamard Transforms by Using Equally Spaced Nodes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 542
Author(s):  
Frank Filbir ◽  
Donatella Occorsio ◽  
Woula Themistoclakis
Keyword(s):  
Simultaneous Approximation ◽  
Bernstein Polynomials ◽  
Reference Interval ◽  
Pointwise Estimates ◽  
Numerical Tests ◽  
Equidistant Points ◽  
Hadamard Transforms ◽  
Boolean Sums ◽  
Generalized Bernstein Polynomials ◽  
Theoretical Results

In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f, supposing to know only the samples of f at equidistant points. As reference interval we consider [ − 1 , 1 ] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.

scholarly journals Generalized Baskakov Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6131-6151
Author(s):  
P.N. Agrawal ◽  
Meenu Goyal
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Statistical Convergence ◽  
Simultaneous Approximation ◽  
Weighted Approximation ◽  
Function Of Bounded Variation ◽  
Convergence Properties ◽  
Almost Everywhere ◽  
Direct Results ◽  
Kantorovich Operators

In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally, we obtain the rate of convergence for functions having a derivative coinciding almost everywhere with a function of bounded variation for these operators.

scholarly journals On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1235
Author(s):  
Bianca Ioana Vasian ◽  
Ștefan Lucian Garoiu ◽  
Cristina Maria Păcurar
Keyword(s):  
Test Functions ◽  
New Class ◽  
Convergence Results ◽  
Error Estimations ◽  
Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

scholarly journals Approximation by Boolean sums of linear operators: Telyakovskiǐ-type estimates

1990 ◽  
Vol 42 (2) ◽  
pp. 253-266 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Upper Bound ◽  
Algebraic Polynomial ◽  
Present Note ◽  
Type Inequality ◽  
Linear Operators ◽  
Polynomial Operators ◽  
Boolean Sums ◽  
General Conditions

In the present note we study the question: “Under which general conditions do certain Boolean sums of linear operators satisfy Telyakovskiǐ-type estimates?” It is shown, in particular, that any sequence of linear algebraic polynomial operators satisfying a Timan-type inequality can be modified appropriately so as to obtain the corresponding upper bound of the Telyakovskiǐ-type. Several examples are included.

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