Various Problems in Approximation by Linear Positive Operators

Prerna Sharma

ISBN 10: 6204750550 / ISBN 13: 9786204750552

Editore: LAP LAMBERT Academic Publishing Mai 2022, 2022

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Neuware -The approximation of functions by algebraic polynomials, trigonometric polynomials and splines, is not only an important topic of mathematical studies but also provides powerful mathematical tools to represent non-arithmetic quantities by arithmetic quantities to achieve the accuracy to a desired degree. The role of linear positive operators is very important in the approximation theory. The theorem given by Weierstrass is the basis of theory of approximation for the functions of real variable and has huge importance in the whole of mathematical analysis.The main purpose of this book is to study the some problems in approximation by linear positive operators. We estimate the rate of convergence for these operators for functions having derivatives of bounded variation. We also studied the new type of Stancu generalization of modified Beta operators and established some moments and recurrence relations as well as study some approximation properties and asymptotic formula for the above operators which gave some better error estimations for the operators by using King's approach. We also find an asymptotic formula and error estimate in terms of higher order modulus of continuity.Books on Demand GmbH, Überseering 33, 22297 Hamburg 132 pp. Englisch.

Codice articolo 9786204750552

Dati bibliografici

• Titolo: Various Problems in Approximation by Linear Positive Operators
• Editore: LAP LAMBERT Academic Publishing Mai 2022
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 6204750550
• ISBN 13: 9786204750552
• Rilegatura: Taschenbuch
• Condizione: Neu

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Riassunto

The approximation of functions by algebraic polynomials, trigonometric polynomials and splines, is not only an important topic of mathematical studies but also provides powerful mathematical tools to represent non-arithmetic quantities by arithmetic quantities to achieve the accuracy to a desired degree. The role of linear positive operators is very important in the approximation theory. The theorem given by Weierstrass is the basis of theory of approximation for the functions of real variable and has huge importance in the whole of mathematical analysis.The main purpose of this book is to study the some problems in approximation by linear positive operators. We estimate the rate of convergence for these operators for functions having derivatives of bounded variation. We also studied the new type of Stancu generalization of modified Beta operators and established some moments and recurrence relations as well as study some approximation properties and asymptotic formula for the above operators which gave some better error estimations for the operators by using King's approach. We also find an asymptotic formula and error estimate in terms of higher order modulus of continuity.