## Topics in Polynomials: Extremal Problems, Inequalities, ZerosThe book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution. |

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### Contents

CHAPTER 1 | 1 |

polynomials | 22 |

CHAPTER 2 | 85 |

CHAPTER 3 | 173 |

RELATED TOPICS | 216 |

CHAPTER 4 | 299 |

CHAPTER 5 | 383 |

WEIGHTED POLYNOMIAL INEQUALITIES | 471 |

CHAPTER 6 | 527 |

in RN | 560 |

CHAPTER 7 | 725 |

GEOMETRIC DESIGN | 757 |

783 | |

803 | |

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### Common terms and phrases

algebraic polynomials Amer Applying Approx approximation arbitrary attained Bernstein best possible bound circle classical coefficients complex conclude conjecture considered constant COROLLARY corresponding curve defined denote depending derivative determined disk equality equation estimate example exists expressed extremal problems fact fixed following inequality following result formula function give given holds inequality integer interesting interval least Lemma Markov Math mention method Milovanović monotonic multiple Namely non-negative norm obtained orthogonal polynomials points polynomial of degree positive Proc proof properties proved the following Rahman real zeros reduces relation Remark respectively roots Russian Saff satisfies sequence showed solution studied subsection Suppose symmetric Szegő Taking THEOREM Theory trigonometric polynomials unique unit Varga variables weight zeros

### Popular passages

Page 711 - RI 02904, but References should be styled and punctuated according to the following examples: 1 . GG Lorentz, The degree of approximation by polynomials with positive coefficients, Math. Ann. 151 (1963), 239-251.