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 issues in analysis. the extent of exposition raises steadily in the course of the ebook, development from a simple requirement of undergraduate skillability to graduate-level sophistication. Appendices supply an advent to (or refresher on) a number of the 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 important for autonomous learn or as a complement to a graduate direction 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 range of attention-grabbing 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.
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A Fixed-Point Farrago (Universitext) by Joel H. Shapiro