Exercises in analysis. II: Nonlinear analysis
type: Item
instance of: scholarly article
title: Exercises in analysis. II: Nonlinear analysis
zbMATH Open document ID: 1351.00006
DOI: 10.1007/978-3-319-27817-9
author: Leszek Gasiński
author: Nikolaos S. Papageorgiou
published in: Problem Books in Mathematics
publication date: 2015-12-09T00:00:00Z
review text: When students today solve mathematical problems, they are not actually solving problems. Rather, they are doing exercises. The book under review trains readers to solve exercises in analysis while demonstrating the beauty and intricacy of this field of mathematics. This book is full of interesting problems. This is a useful collection of problems (with complete solutions) in pure and applied nonlinear functional analysis. The problems are selected so that working each one will teach you something; they are not drill, and do not yield to the obvious standard methods. The book covers a wide range of topics and would be suitable for supplementing an upper undergraduate course in analysis. The volume is also addressed to graduate students and to researchers in pure and applied analysis. The content of this book is divided into the following five chapters: 1. Function spaces; 2. Nonlinear and multivalued maps; 3. Smooth and nonsmooth calculus; 4. Degree theory and fixed point theory; 5. Variational and topological methods. At least 200 well selected problems are presented in the every of the first four chapters (176 exercises in the fifth chapter). The relevant main abstract results are summarized at the beginning of each chapter. The problems are challenging and accessible and they are ranging from easy to difficult, with level of difficulty designated by the authors. The higher problems are not more difficult, but require more advanced mathematics. Working through the problems will teach you a lot about the relevant results in pure and applied nonlinear functional analysis. The solutions run about a quarter of a page each (with a lot of variation), so they are not extremely difficult or especially easy, once you have hit upon the right facts to use. The book provides a good mix of abstract and concrete problems. The concrete problems are not simple drill and require some ingenuity and a good understanding of analytic concepts. Overall, this volume is an excellent gatew…
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 00A07
Mathematics Subject Classification ID: 26-01
Mathematics Subject Classification ID: 28-01
Mathematics Subject Classification ID: 54-01
Mathematics Subject Classification ID: 46-01
Mathematics Subject Classification ID: 60-01
zbMATH DE Number: 6518674
zbMATH Keywords: metric space
zbMATH Keywords: topological space
zbMATH Keywords: nonlinear map
zbMATH Keywords: nonsmooth calculus
zbMATH Keywords: degree theory
zbMATH Keywords: variational methods
zbMATH Keywords: topological methods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-27817-9
OpenAlex ID: W4236720356
description: scientific article; zbMATH DE number 6518674