Gupta V., Tachev G. Approximation with Positive Linear Operators and Linear Combinations

Springer International Publishing AG, 2017. — 193 p. — (Developments in Mathematics 50). — ISBN: 3319587943.This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln, direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions.Moments and Combinations of Positive Linear Operators
Direct Estimates for Approximation by Linear Combinations
Inverse Estimates and Saturation Results for Linear Combinations
Voronovskaja-Type Estimates
Pointwise Estimates for Linear Combinations
Voronovskaja’s Theorem in Terms of Weighted Modulus of Continuity
Direct Estimates for Some New Operators
Convergence for Operators Based on Pˇaltˇanea Basis