Search results for " 41A36"

showing 5 items of 5 documents

Better numerical approximation by Durrmeyer type operators

2018

The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally, the theoretical results are analyzed by numerical examples.

41A25 41A36Applied Mathematics010102 general mathematicsConstruct (python library)Numerical Analysis (math.NA)Type (model theory)Object (computer science)01 natural sciences010101 applied mathematicsMathematics (miscellaneous)Operator (computer programming)Rate of convergenceNumerical approximationFOS: MathematicsApplied mathematicsMathematics - Numerical Analysis0101 mathematicsMathematics
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Elementary hypergeometric functions, Heun functions, and moments of MKZ operators

2019

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.

Pure mathematicsAlgebra and Number TheorySeries (mathematics)Applied Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEsNumerical Analysis (math.NA)Type (model theory)33C05 33C90 33E30 41A3601 natural sciencesSecond order moments010101 applied mathematicsComputational MathematicsMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsElementary functionHigher order momentsGeometry and TopologyMathematics - Numerical Analysis0101 mathematicsHypergeometric functionAnalysisMathematics
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Better approximation of functions by genuine Bernstein-Durrmeyer type operators

2018

The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.

41A25 41A36FOS: MathematicsNumerical Analysis (math.NA)Mathematics - Numerical Analysis
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Estimates for the differences of positive linear operators and their derivatives

2019

The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.

41A25 41A36Applied MathematicsNumerical analysisLinear operatorsNumerical Analysis (math.NA)010103 numerical & computational mathematics01 natural sciencesModulus of continuity010101 applied mathematicsSection (fiber bundle)Mathematics - Classical Analysis and ODEsBounded functionTheory of computationClassical Analysis and ODEs (math.CA)FOS: MathematicsOrder (group theory)Applied mathematicsMathematics - Numerical Analysis0101 mathematicsAlgebra over a fieldMathematics
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Perturbed Bernstein-type operators

2018

The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and second modulus of continuity are given. Also the asymptotic formulas for the new operators are proved.

Pure mathematicsAlgebra and Number Theory41A25 41A36010102 general mathematicsNumerical Analysis (math.NA)Type (model theory)01 natural sciencesModulus of continuityMathematik0103 physical sciencesFOS: Mathematics010307 mathematical physicsMathematics - Numerical Analysis0101 mathematicsMathematical PhysicsAnalysisMathematics
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