Fixed Point Theorems with Applications

图书简介

As a very important part of nonlinear analysis, fixed point theory plays a key role in solvability of many complex systems from mathematics applied to chemical reactors, neutron transport, population biology, infectious diseases, economics, applied mechanics, and more.The main aim of Fixed Point Theorems with Applications is to explain new techniques for investigation of different classes of ordinary and partial differential equations. The development of the fixed point theory parallels the advances in topology and functional analysis. Recent research has investigated not only the existence but also the positivity of solutions for various types of nonlinear equations. This book will be of interest to those working in functional analysis and its applications.Combined with other nonlinear methods such as variational methods and the approximation methods, the fixed point theory is powerful in dealing with many nonlinear problems from the real world.The book can be used as a textbook to develop an elective course on nonlinear functional analysis with applications in undergraduate and graduate programs in mathematics or engineering programs.

Preface 1 Preliminaries 1.1 Normed Linear Spaces 1.2 Banach Spaces 1.3 Linear Operators in Normed Vector Spaces 1.4 Inverse Operators 1.5 Measures of Noncompactness 1.5.1 The General Setting 1.5.2 Case of Normed Spaces 1.6 Related Maps 1.6.1 k-Set Contractions 1.6.2 Nonexpansive and Expansive Maps 1.7 Ascoli-Arzelà Theorem 1.7.1 Ascoli-Arzelà Theorem : a First Version 1.7.2 Applications 1.7.3 General Forms of Ascoli-Arzelà Theorem 1.8 Corduneanu-Avramescu Compactness Criterion in C¿ 1.8.1 Main Results 1.8.2 Application 1 1.8.3 Application 2 1.9 Przeradzki’s Compactness Criterion in BC (R¿Y) 1.9.1 Main Result 1.9.2 Application 1.10 Compactness Criterion in C ([0¿ Y)¿Rn) 1.11 Compactness Criteria in BC (X¿R) 1.11.1 The Stone-Cech Compactification 1.11.2 Bartles’s Compactness Criterion and Consequences 1.12 Higher-order Derivative Spaces 1.12.1 The Compact Case 1.12.2 The Noncompact Case 1.13 Zima’s Compactness Criterion 1.13.1 Main Result 1.13.2 Application 1 1.13.3 Application 2 1.14 Cones and Partial Order Relations 2 Fixed Point Index for Sums of Two Operators 2.1 Auxiliary Results 2.2 Fixed Point Index on Cones 2.2.1 The Case Where T is an h-Expansive Mapping and F is a k-Set Contraction with 0

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Fixed Point Theorems with Applications 不动点定理及其应用 代数学

Fixed Point Theorems with Applications

不动点定理及其应用
代数学