Nonlinear Functional Analysis in Banach Spaces and Banach Algebras

This is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and algebras. The authors present several extensions of Schauder’s and Krasnosel’skii’s fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point. In addition, the book describes applications of fixed point theory to diverse equations.