A Fixed-Point Farrago (Universitext)

December 8, 2020
A Fixed-Point Farrago (Universitext)

Acts as a perfect book for Graduate-level Fixed-PointTheoryCovers all major Fixed-Point theories in detailIntroduces Fixed-Point Theory and correlates it to severaltopics in Analysis——————————This text provides an introduction to some of the best-knownfixed-point theorems, with an emphasis on their interactions withtopics in analysis. The level of exposition increases graduallythroughout the book, building from a basic requirement ofundergraduate proficiency to graduate-level sophistication.Appendices provide an introduction to (or refresher on) some of theprerequisite material and exercises are integrated into the text,contributing to the volume’s ability to be used as a self-containedtext. Readers will find the presentation especially useful forindependent study or as a supplement to a graduate course infixed-point theory.The material is split into four parts: the first introduces theBanach Contraction-Mapping Principle and the Brouwer Fixed-PointTheorem, along with a selection of interesting applications; thesecond focuses on Brouwer’s theorem and its application to JohnNash’s work; the third applies Brouwer’s theorem to spaces ofinfinite dimension; and the fourth rests on the work of Markov,Kakutani, and Ryll–Nardzewski surrounding fixed points for familiesof affine maps.