This is the first book in an incredible five volume work on nonlinear functional analysis and its applications the volumes i fixed point theorems iia linear monotone operators iib nonlinear montone operators iii variational methods and optimization iv applications to mathematical physics are together over 3700 pages in length. Felix klein there exists the remarkable possibility that one can master a subject mathemati cally without really understanding its essence albert einstein dont give us nonlinear functional analysis and its applications i fixed point theorems eberhard zeidler springer. This single volume textbook covers the fundamentals of linear and nonlinear functional analysis illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory fixed point theorems nonlinear functional analysis . Nonlinear functional analysis and its applications vol 1 fixed point theorems eberhard zeidler the significance of the banach fixed point theorem 14 applications to nonlinear equations 15 accelerated convergence and newtons method 16 the picard lindelof theorem 17 the main theorem for iterative methods for linear . Functional analysis and its applications i fixed point theorems translated by peter r wadsack the significance of the banach fixed point theorem 14 applications to nonlinear equations 15 accelerated convergence and newtons method the surjective implicit function theorem 176 nonlinear systems of equations subimmersions and
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