Lipschitz Functions

The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces.
The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.

Scopul acestei carti este de a prezenta diverse fatete ale teoriei si aplicatiilor functiilor Lipschitz, incepand cu clasic si culminand cu cateva rezultate recente. Printre subiectele incluse mentionam: caracterizarile functiilor Lipschitz si relatiile cu alte clase de functii, rezultatele extensiilor pentru functiile Lipschitz si partitiile Lipschitz ale unitatii, spatiile Banach fara Lipschitz si aplicatiile lor, proprietatile de compactitate ale operatorilor Lipschitz, rezultatele de tip Bishop-Phelps pentru Functionalitati Lipschitz, aplicatii la cea mai buna aproximare in spatii metrice si in spatii liniare metrice, norma Kantorovich-Rubinstein si aplicatii la dualitate in problema de transport optima, cartografii Lipschitz pe spatii geodezice. Conditiile preliminare sunt rezultate de baza in analiza reala, analiza functionala, teoria masurilor inclusiv masuri vectoriale) si topologie, care, pentru comoditatea cititorului, sunt analizate in primul capitol al cartii.