Exercises in Analysis

This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods.Each of five topics corresponds to a different chapter withinclusion of the basic theory and accompanying main definitions and results,followed by suitable comments and remarks for better understanding of thematerial. Exercises/problems are presented for each topic, withsolutions available at the end of each chapter. The entire collection of exercisesoffers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is thefirst of its kind and is accessible to a wide readership. Graduate students willfind the collection of problems valuable in preparation for their preliminary orqualifying exams as well as for testing their deeper understanding of thematerial. Exercises are denoted by degree of difficulty. Instructors teachingcourses that include one or all of the above-mentioned topics will find theexercises of great help in course preparation. Researchers in analysis may findthis Work useful as a summary of analytic theories published in one accessiblevolume.