Exercises in Analysis

1. Front Matter

   Pages i-viii

   PDF

2. Function Spaces

   • Leszek Gasiński, Nikolaos S. Papageorgiou

   Pages 1-216

3. Nonlinear and Multivalued Maps

   • Leszek Gasiński, Nikolaos S. Papageorgiou

   Pages 217-408

4. Smooth and Nonsmooth Calculus

   • Leszek Gasiński, Nikolaos S. Papageorgiou

   Pages 409-616

5. Degree Theory and Fixed Point Theory

   • Leszek Gasiński, Nikolaos S. Papageorgiou

   Pages 617-803

6. Variational and Topological Methods

   • Leszek Gasiński, Nikolaos S. Papageorgiou

   Pages 805-1034

7. Back Matter

   Pages 1035-1062

   PDF

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 with inclusion of the basic theory and accompanying main definitions and results,
followed by suitable comments and remarks for better understanding of the material. Exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.


This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.

• degree theory
• fixed point theory
• function spaces
• nonlinear and multivalued maps
• smooth and nonsmooth calculus
• variational and topological methods

“This is a truly stunning collection of material which is certainly most welcome.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 192 (1), 2020)

“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 volume is also addressed to graduate students and to researchers in pure and applied analysis. … this volume is an excellent gateway to the culture of problem solving. It is challenging and rewarding. The book shines a new light on mathematics and engages readers with its wonderful insights and problems.” (Vicenţiu D. Rădulescu, zbMATH, 1351.00006, 2017)

• Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland

  Leszek Gasiński

• National Technical University Department of Mathematics, Athens, Greece

  Nikolaos S. Papageorgiou

Leszek Gasińksi is the Chair of Optimization and Control Theory in the Institute of Computer Science at Jagiellonian University in Krakow, Poland. He is the co-author, along with Nikolaos S. Papageorgiou, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006). Nikolaos S. Papageorgiou is a Professor of Mathematics in the School of Applied Mathematical and Physical Sciences at National Technical University in Athens, Greece. He is the co-author, along with Leszek Gasińksi, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006).

Policies and ethics