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.