Khamsi M.A., Kirk W.A. An Introduction to Metric Spaces and Fixed Point Theory

John Wiley & Sons, 2001. — 320 pages. ISBN: 0471418250Presents up-to-date Banach space results.
Features an extensive bibliography for outside reading.
Provides detailed exercises that elucidate more introductory material.This text is primarily an introduction to metric spaces and fixed point theory. It is intended to be especially useful to those who might not have ready access to other sources, or to groups of people with diverse mathematical backgrounds. Because of this the text is self-contained. Introductory properties of metric spaces and Banach spaces are included, and an appendix contains a summary of the concepts of set theory (Zorn's Lemma, Tychonoff's Theorem, transfinite induction, etc.) that might be encountered elsewhere in the text. Most of the text should be accessible to reasonably mature students who have had very little training in mathematics beyond calculus. In particular a very elementary treatment of Brouwer's Theorem is given in Chapter
7. At the same time later chapters of the book contain a large amount of material that might be of interest to more advanced students and even to serious scholars.