By Joel H. Shapiro
This textual content offers an advent to a couple of the best-known fixed-point theorems, with an emphasis on their interactions with issues in analysis. the extent of exposition raises progressively in the course of the booklet, construction from a uncomplicated requirement of undergraduate talent to graduate-level sophistication. Appendices offer 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 beneficial for autonomous research 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, in addition to a variety of fascinating functions; the second one specializes in Brouwer’s theorem and its program to John Nash’s paintings; the 3rd applies Brouwer’s theorem to areas of endless size; and the fourth rests at the paintings of Markov, Kakutani, and Ryll–Nardzewski surrounding mounted issues for households of affine maps.