Nonlinear Analysis and Variational Problems

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. They cover some important areas of nonlinear analysis and variational problems.

The papers published in this volume focus on some of the most recent devel- ments in complementarity theory, variational principles, stability theory of fu- tional equations, nonsmooth optimization, and various other important topics of nonlinear analysis and optimization. This volume was initially planned to celebrate Professor George Isac's 70th birthday by bringing together research scientists from mathematical domains which have long bene ted from Isac's active research passion. Unfortunately, George Isac passed away in February 2009 at the age of 69. George Isac received his Ph. D. in 1973 from the Institute of Mathematics of the Romanian Academy of Sciences. He made outstanding contributions in s- eral branches of pure and applied mathematics, including complementarity theory, variational inequalities, xed point theory, scalar and vector optimization, theory of cones, eigenvalue problems, convex analysis, variational principles and regulari- tion methods, as well as a number of other topics. In his long and outstanding career, he wrote more than 200 papers and 13 books. Professor Isac was an avid traveler who visited more than 70 universities around the globe and delivered approximately 180 research presentations. He also authored seven books on poetry. During his s- enti c career he collaborated with numerous mathematicians. His research papers contain very deep, original and beautiful results. Through his signi cant contri- tions, he earned a distinguished position and became an internationally renowned leading scholar in his research elds.

Contains 25 research papers with a limited number of survey papers by leading mathematicians in some important areas of nonlinear analysis and variational problems Presents recent developments in complementarity theory, variational problems, stability theory of functional equations, and various other topics of nonlinear analysis and optimization Includes properties of nuclear cones and variational principles Appeals to a broad audience of graduate students, researchers, and practitioners in the fields of pure and applied mathematics, social sciences, economics, operations research, engineering, and other related sciences Includes supplementary material: sn.pub/extras

Inhalt
I Nonlinear Analysis.- Discrete Approximation Processes of King#x2019;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#x002A;-Tensor Products of W#x002A;-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#x2013;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#x2013;Expansion Critical Point Theorems in Conical Shells.- Gronwall Lemma Approach to the Hyers#x2013;Ulam#x2013;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.