Synopses & Reviews
This text introduces the methods of applied functional analysis and applied convexity. Suitable for advanced undergraduates and graduate students of mathematics, science, and technology, it focuses on the solutions to two closely related problems. The first concerns finding roots of systems of equations and operative equations in a given region. The second involves extremal problems of minimizing or maximizing functions defined on subsets of finite and infinite dimensional spaces. Rather than citing practical algorithms for solving problems, this treatment provides the tools for studying problem-related algorithms.
Topics include iterations and fixed points, metric spaces, nonlinear programming, polyhedral convex programming, and infinite convex programming. Additional subjects include linear spaces and convex sets and applications to integral equations. Students should be familiar with advanced calculus and linear algebra. As an introduction to elementary functional analysis motivated by application, this volume also constitutes a helpful reference for theoretically minded engineers, scientists, and applied mathematicians.
This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. Topics include iterations and fixed points, metric spaces, nonlinear programming, applications to integral equations, and more. 1967 edition.
Table of Contents
Preface I. Roots and Extremal Problems A. Iterations and Fixed Points B. Metric Spaces C. Miscellany D. Gradient Techniques II. Constraints A. Nonlinear Programming B. Polyhedral Convex Programming C. Infinite Convex Programming III. Infinite Dimensional Problems A. Linear Spaces and Convex Sets B. Miscellany C. Roots and Extremals D. Applications to Integral Equations E. An Application to Control Theory Notes and Bibliographic Material Index