Nonlinear evolution and difference equations of monotone type in Hilbert spaces. (2019)

• Record Type: Book
• Further Information: Note: Behzad Djafari-Rouhani (Department of Mathematical Sciences, University of Texas at El Paso, Texas, USA), Hadi Khatibzadeh (Department of Mathematics, Zanjan University, Zanjan, Iran).
• Authors: Djafari-Rouhani, Behzad; Khatibzadeh, Hadi
• Contents: Cover; Title Page; Copyright Page; Table of Contents; Preface; PART I: PRELIMINARIES; 1: Preliminaries of Functional Analysis; 1.1 Introduction to Hilbert Spaces; 1.2 Weak Topology and Weak Convergence; 1.3 Reflexive Banach Spaces; 1.4 Distributions and Sobolev Spaces; 1.4.1 Vector-valued Functions; 1.4.2 Lp Spaces; 1.4.3 Scalar Distributions and Sobolev Spaces; 1.4.4 Vector Distributions and Sobolev Spaces; 2: Convex Analysis and Subdifferential Operators; 2.1 Introduction; 2.2 Convex Sets and Convex Functions; 2.3 Continuity of Convex Functions; 2.4 Minimization Properties 2.5 Fenchel Subdifferential2.6 The Fenchel Conjugate; 3: Maximal Monotone Operators; 3.1 Introduction; 3.2 Monotone Operators; 3.3 Maximal Monotonicity; 3.4 Resolvent and Yosida Approximation; 3.5 Canonical Extension; PART II: EVOLUTION EQUATIONS OF MONOTONE TYPE; 4: First Order Evolution Equations; 4.1 Introduction; 4.2 Existence and Uniqueness of Solutions; 4.3 Periodic Forcing; 4.4 Nonexpansive Semigroup Generated by a Maximal Monotone Operator; 4.5 Ergodic Theorems for Nonexpansive Sequences and Curves; 4.5.1 Almost Nonexpansive Sequences; 4.5.2 Almost Nonexpansive Curves 4.6 Weak Convergence of Solutions and Means4.7 Almost Orbits; 4.8 Sub-differential and Non-expansive Cases; 4.9 Strong Ergodic Convergence; 4.10 Strong Convergence of Solutions; 4.11 Quasi-convex Case; 5: Second Order Evolution Equations; 5.1 Introduction; 5.2 Existence and Uniqueness of Solutions; 5.2.1 The Strongly Monotone Case; 5.2.2 The Non Strongly Monotone Case; 5.3 Two Point Boundary Value Problems; 5.4 Existence of Solutions for the Nonhomogeneous Case; 5.5 Periodic Forcing; 5.6 Square Root of a Maximal Monotone Operator; 5.7 Asymptotic Behavior; 5.7.1 Ergodic Convergence 5.7.2 Weak Convergence5.7.3 Strong Convergence; 5.7.4 Subdifferential Case; 5.8 Asymptotic Behavior for Some Special Nonhomogeneous Cases; 5.8.1 Case C ≤ 0; 5.8.2 The Case C > 0; 6: Heavy Ball with Friction Dynamical System; 6.1 Introduction; 6.2 Minimization Properties; PART III: DIFFERENCE EQUATIONS OF MONOTONE TYPE; 7: First Order Difference Equations and Proximal Point Algorithm; 7.1 Introduction; 7.2 Boundedness of Solutions; 7.3 Periodic Forcing; 7.4 Convergence of the Proximal Point Algorithm; 7.5 Convergence with Non-summable Errors; 7.6 Rate of Convergence 8: Second Order Difference Equations8.1 Introduction; 8.2 Existence and Uniqueness; 8.3 Periodic Forcing; 8.4 Continuous Dependence on Initial Conditions; 8.5 Asymptotic Behavior for the Homogeneous Case; 8.5.1 Weak Ergodic Convergence; 8.5.2 Strong Ergodic Convergence; 8.5.3 Weak Convergence of Solutions; 8.5.4 Strong Convergence of Solutions; 8.6 Subdifferential Case; 8.7 Asymptotic Behavior for the Non-Homogeneous Case; 8.7.1 Mean Ergodic Convergence; 8.7.2 Weak Convergence of Solutions; 8.7.3 Strong Convergence of Solutions; 8.8 Applications to Optimization
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 515/.35; Evolution equations, Nonlinear; Differential equations, Nonlinear; Differential equations; Hilbert space; Differential equations; Differential equations, Nonlinear; Evolution equations, Nonlinear; Hilbert space; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9780429156908; 0429156901; 9780429528880; 0429528884; 9781482228199
• Related ISBNs: 9781482228182; 1482228181; 148222819X
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.