CONTRIBUTIONS TO NONLINEAR FUNCTIONAL ANALYSIS

By J. PALAD

CONTENTS BASIC TOPOLOGY BASIC NOTIONS SEPARATION AND COUNTABILITY PROPERTIES – CONVERGENCE WEAK, PRODUCT, AND QUOTIENT TOPOLOGIES CONNECTEDNESS AND COMPACTNESS METRIC SPACES – BAIRE CATEGORY FUNCTION SPACES SEMICONTINUOUS FUNCTIONS – MISCELLANEOUS NOTIONS REMARKS MEASURE THEORY BASIC NOTIONS, MEASURES, AND OUTER MEASURES MEASURABLE FUNCTIONS – INTEGRATION CONVERGENCE THEOREMS AND LP-SPACES SIGNED MEASURES AND RADON–NIKODYM THEOREM REGULAR AND RADON MEASURES ANALYTIC (SOUSLIN) SETS SELECTION AND PROJECTION THEOREMS HAUSDORFF MEASURES BASIC FUNCTIONAL ANALYSIS TOPOLOGICAL VECTOR SPACES, HAHN–BANACH THEOREM THREE FUNDAMENTAL THEOREMS WEAK AND WEAK* TOPOLOGIES SEPARABLE AND REFLEXIVE BANACH SPACES HILBERT SPACES BOUNDED AND UNBOUNDED LINEAR OPERATORS COMPACT OPERATORS – FREDHOLM OPERATORS BANACH SPACES OF FUNCTIONS AND MEASURES LP-SPACES LEBESGUE–BOCHNER SPACES FUNCTIONS OF BOUNDED VARIATIONS ABSOLUTELY CONTINUOUS FUNCTIONS SOBOLEV SPACES SPACES OF MEASURES YOUNG MEASURES SEMIGROUPS OF OPERATORS GENERALIZED ORLICZ SPACES CONVEX FUNCTIONS – NONSMOOTH ANALYSIS CONVEX FUNCTIONS – CONTINUITY PROPERTIES DIFFERENTIABILITY OF CONVEX FUNCTIONS CONJUGATE FUNCTIONS – CONVEX SUBDIFFERENTIAL PROXIMINAL AND CHEBYSHEV SETS SMOOTHNESS OF THE NORM MULTIFUNCTIONS – INTEGRAL FUNCTIONALS LIPSCHITZ AND LOCALLY LIPSCHITZ FUNCTIONS NONLINEAR ANALYSIS OPERATORS OF MONOTONE TYPE BROUWER DEGREE LERAY–SCHAUDER DEGREE FIXED POINT THEORY METRIC FIXED POINT THEORY TOPOLOGICAL FIXED POINT THEORY FIXED POINT INDEX VARIATIONAL PRINCIPLES VARIATIONAL CONVERGENCE NONLINEAR OPERATORS, IDENTITIES AND INEQUALITIES