Various Problems in Approximation by Linear Positive Operators

Sharma, Prerna; Sharma, Diwaker; Singh, Bhim

ISBN 10: 6204750550 / ISBN 13: 9786204750552

Published by LAP LAMBERT Academic Publishing, 2022

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Bibliographic Details

• Title: Various Problems in Approximation by Linear Positive Operators
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2022
• Language: English
• ISBN 10: 6204750550
• ISBN 13: 9786204750552
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.