By Joel H. Shapiro
This textual content presents an creation to a few of the best-known fixed-point theorems, with an emphasis on their interactions with themes in analysis. the extent of exposition raises progressively in the course of the e-book, construction from a easy requirement of undergraduate talent to graduate-level sophistication. Appendices supply an advent to (or refresher on) a number of the prerequisite fabric and routines 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 particularly precious for self sufficient learn or as a complement to a graduate path in fixed-point theory.
The fabric is divided into 4 elements: the 1st introduces the Banach Contraction-Mapping precept and the Brouwer Fixed-Point Theorem, in addition to a variety of fascinating purposes; 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 limitless measurement; and the fourth rests at the paintings of Markov, Kakutani, and Ryll–Nardzewski surrounding mounted issues for households of affine maps.
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Additional resources for A Fixed-Point Farrago (Universitext)
A Fixed-Point Farrago (Universitext) by Joel H. Shapiro