By Joel H. Shapiro
This textual content presents an advent to a few of the best-known fixed-point theorems, with an emphasis on their interactions with themes in research. the extent of exposition raises steadily in the course of the ebook, development from a uncomplicated requirement of undergraduate talent to graduate-level sophistication. Appendices supply an advent to (or refresher on) the various prerequisite fabric and workouts are built-in into the textual content, contributing to the volume’s skill for use as a self-contained textual content. Readers will locate the presentation specifically worthy for autonomous examine or as a complement to a graduate direction in fixed-point theory.
The fabric is divided into 4 components: the 1st introduces the Banach Contraction-Mapping precept and the Brouwer Fixed-Point Theorem, besides a variety of attention-grabbing functions; the second one makes a speciality of Brouwer’s theorem and its software to John Nash’s paintings; the 3rd applies Brouwer’s theorem to areas of endless measurement; and the fourth rests at the paintings of Markov, Kakutani, and Ryll–Nardzewski surrounding mounted issues for households of affine maps.