Shape-Preserving Approximation By Real Univariate Polynomials

In this chapter we present the main results concerning shape-preserving approximation by polynomials for real functions of one real variable, defined on compact subintervals of the real axis. There is a very rich literature dedicated to this topic that would suffice to write a separate book. Due to this fact, it was impossible for me to avoid the more pronounced survey-like character of this chapter. Also, for the proofs of some main results that are very technical and long, we will present here only their most important ideas and steps.


Polynomial Approximation Bernstein Polynomial Pointwise Estimate Uniform Norm Convex Approximation 
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© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2008

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