A Fixed-Point Farrago (Universitext) by Joel H. Shapiro

By Joel H. Shapiro

This textual content presents an creation to a couple of the best-known fixed-point theorems, with an emphasis on their interactions with subject matters in analysis.  the extent of exposition raises steadily in the course of the booklet, construction from a easy requirement of undergraduate skillability to graduate-level sophistication. Appendices supply an creation to (or refresher on) many 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 specifically important for autonomous 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, besides a variety of fascinating purposes; 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 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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