Fixed Point Theorems and Applications

Vittorino Pata completed his PhD in Pure Mathematics at Indiana University, USA in December 1994. Since 2000, he has been a Professor of Mathematical Analysis at the Politecnico di Milano, Italy. His research interests touch several areas of pure and applied mathematics, including ordinary and partial differential equations (with particular emphasis on the asymptotic behavior of solutions), infinite-dimensional dynamical systems, real and functional analysis, operator theory, and noncommutative probability.

1 The Banach contraction principle 7.- 2 The Boyd-Wongtheorem 13.- 3 Further extensions of the contraction principle 16.- 4 Weak contractions 23.- 5 Contractions of -type 29.- 6 Sequences of maps  and fixed points 36.- 7 Fixed points of non-expansive maps 39.- 8 The Riesz mean ergodic theorem 42.- 9 The Brouwer fixed point theorem 46.- 10 The Schauder-Tychono fixed point theorem 50.- 11 Further consequences of the Schauder-Tychono theorem 55.- 12 TheMarkov-Kakutani theorem 60.- 13 TheKakutani-Ky Fan theorem 62.- 14 The implicit function theorem 70.- 15 Location of zeros 75.- 16 Ordinary di erential equations in Banach spaces 78.- 17 The Lax-Milgram lemma 89.- 18 An abstract elliptic problem 97.- 19 Semilinear evolution equations 101.- 20 An abstract parabolic problem 108.- 21 The invariant subspace problem 114.- 22 Measure preserving maps on compact Hausdor spaces 118.- 23 Invariant means on semigroups 120.- 24 Haar measures 123.- 25 Game theory 130.- 26 Problems.

"This book is certainly one of the best. It should be quite useful to anybody interested in the theory, methods, and applications of nonlinear functional analysis, in particular to students during their masters studies (il maledetto 3+2, una grossa sciocchezza politica che fa soffrire tanti studenti)." (Jürgen Appell, zbMATH 1448.47001, 2020)
"This is a good reference book on the applications of fixed point theory to other fields in mathematics, optimization theory, economics, engineering, and image science. ... I must point out that this book lets researchers get their required knowledge on fixed points in a short time." (Lai-Jiu Lin, Mathematical Reviews, May, 2020)
"It could be used as a textbook for a somewhat unusual functional analysis course, or for a real analysis coursethat introduces functional analysis. It would also be good preparation for a course in nonlinear partial differential equations or control theory." (John D. Cook, MAA Reviews, October 6, 2019)