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. Strong converse
inequalities of Type A in terminology of Ditzian-Ivanov for linear
combinations of Bernstein and Bernstein-Kantorovich operators and
various Voronovskaja-type estimates for some linear combinations
are analyzed and explained. Graduate students and researchers in
approximation theory will find the list of open problems in
approximation of linear combinations useful. The book serves as a
reference for graduate and postgraduate courses as well as a basis
for future study and development.
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