UPC: 9783319802510 | Universitext: A Fixed-Point Farrago (Paperback)

UPC lookup results for: 9783319802510 | Universitext: A Fixed-Point Farrago (Paperback)

This text provides an introduction to some of the best-known fixed-point theorems with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text contributing to the volume s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem along with a selection of interesting applications; the second focuses on Brouwer s theorem and its application to John Nash s work; the third applies Brouwer s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov Kakutani and Ryll-Nardzewski surrounding fixed points for families of affine maps.