Nonlinear Analysis and Variational Problems: In Honor of George Isac / Edition 1by Panos M. Pardalos
Pub. Date: 11/02/2009
Publisher: Springer New York
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at… See more details below
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
"Nonlinear Analysis and Variational Problems" is organized into two parts. Part I, Nonlinear Analysis, centers on stability issues for functional equations, fixed point theorems, critical point theorems, W*-algebras, the Brezis–Browder principle, and related topics. Part II, Variational Problems, addresses several important aspects of optimization and variational methods. This includes equilibrium problems, projected dynamical system, set-valued and set-semidefinite optimization, variational inequalities, variational principles, complementarity problems, and problems in optimal control.
In the last few decades, the theory of complementarity, functional stability and variational principles have provided a unified framework for dealing with a wide range of problems in diverse branches of pure and applied mathematics, such as finance, operations research, economics, network analysis, control theory, biology, and others. This volume is well-suited to graduate students as well as researchers and practitioners in the fields of pure and applied mathematics, social sciences, economics, operations research, engineering, and related sciences.
Table of ContentsI Nonlinear Analysis.- Discrete Approximation Processes of King’s Type.- Isometrics in Non-Archimedean Strictly Convex and Strictly 2-Convex 2-Normed Spaces.- Fixed Points and Generalized Stability for -Additive Mappings of Isac-Rassias Type.- A Remark on W*-Tensor Products of W*-Algebras.- The Perturbed Median Principle for Integral Inequalities with Applications.- Stability of a Mixed Type Additive, Quadratic, Cubic and Quartic Functional Equation.- -Aditive Mappings and Hyers–Ulam Stability.- The Stability and Asymptotic Behavior of Quadratic Mappings on Restricted Domains.- A Fixed Point Approach to the Stability of a Logarithmic Functional Equation.- Fixed Points and Stability of the Cauchy Functional Equation in Lie -Algebras.- Fixed Points and Stability of Functional Equations.- Compression–Expansion Critical Point Theorems in Conical Shells.- Gronwall Lemma Approach to the Hyers–Ulam–Rassias Stability of an Integral Equation.- Brezis-Browder Principles and Applications.- II Variational Problems.- A Generalized Quasi-Equilibrium Problem.- Double-Layer and Hybrid Dynamics of Equilibrium Problems: Applications to Markets of Environmental Products.- A Panoramic View on Projected Dynamical Systems.- Foundations of Set-Semidefinite Optimization.- On the Envelope of a Variational Inequality.- On the Nonlinear Generalized Ordered Complementarity Problem.- Optimality Conditions for Several Types of Efficient Solutions of Set-Valued Optimization Problems.- Mean Value Theorems for the Scalar Derivative and Applications.- Application of a Vector-Valued Ekeland-Type Variational Principle for Deriving Optimality Conditions.- Nonlinear Variational Methods for Estimating Effective Properties of Multiscale Materials.- On Common Linear/Quadratic Lyapunov Functions for Switched Linear Systems.- Nonlinear Problems in Mathematical Programming and Optimal Control.- On Variational Inequalities Involving Mappings of Type (S).- Completely Generalized Co-complementarity Problems Involving -Relaxed Accretive Operators with Fuzzy Mappings.- Generating Eigenvalue Bounds Using Optimization.
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