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The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations. Contents: Linear Complex Vector Functional Equations: General Classes of Cyclic Functional Equations; Functional Equations with Operations Between Arguments; Functional Equations with

Functional equations. --- Vector fields. --- Vector valued functions. --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Direction fields (Mathematics) --- Fields, Direction (Mathematics) --- Fields, Slope (Mathematics) --- Fields, Vector --- Slope fields (Mathematics) --- Vector analysis --- Equations, Functional

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This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning. This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.

Linear topological spaces. --- Mathematical optimization. --- Vector spaces. --- Management --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Business & Economics --- Management Theory --- Operations Research --- Vector valued functions. --- Functions, Vector --- Functions, Vector valued --- Business. --- Operations research. --- Decision making. --- Management science. --- Business and Management. --- Operation Research/Decision Theory. --- Optimization. --- Operations Research, Management Science. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional analysis --- Functions of real variables

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This book contains nine well-organized survey articles by leading researchers in positivity, with a strong emphasis on functional analysis. It provides insight into the structure of classical spaces of continuous functions, f-algebras, and integral operators, but also contains contributions to modern topics like vector measures, operator spaces, ordered tensor products, non-commutative Banach function spaces, and frames. Contributors: B. Banerjee, D.P. Blecher, K. Boulabiar, Q. Bu, G. Buskes, G.P. Curbera, M. Henriksen, A.G. Kusraev, J. Mart??-nez, B. de Pagter, W.J. Ricker, A.R. Schep, A. Tri

Ordered algebraic structures. --- Vector valued functions. --- Functional analysis. --- Positive operators. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Operators, Positive --- Linear operators --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Global analysis (Mathematics). --- Algebra. --- Operator theory. --- Cell aggregation --- Economics. --- Analysis. --- Order, Lattices, Ordered Algebraic Structures. --- Functional Analysis. --- Operator Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Economics, general. --- Mathematics. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematics --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Manifolds (Mathematics). --- Complex manifolds. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- 517.1 Mathematical analysis

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V-INVEX FUNCTIONS AND VECTOR OPTIMIZATION summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past several decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. V-invex functions are areas in which there has been much interest because it allows researchers and practitioners to address and provide better solutions to problems that are nonlinear, multi-objective, fractional, and continuous in nature. Hence, V-invex functions have permitted work on a whole new class of vector optimization applications. There has been considerable work on vector optimization by some highly distinguished researchers including Kuhn, Tucker, Geoffrion, Mangasarian, Von Neuman, Schaiible, Ziemba, etc. The authors have integrated this related research into their book and demonstrate the wide context from which the area has grown and continues to grow. The result is a well-synthesized, accessible, and usable treatment for students, researchers, and practitioners in the areas of OR, optimization, applied mathematics, engineering, and their work relating to a wide range of problems which include financial institutions, logistics, transportation, traffic management, etc.

Convex functions. --- Vector valued functions. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Functions, Convex --- Mathematics. --- Operations research. --- Management. --- Optimization. --- Applications of Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Operations Research/Decision Theory. --- Operations Research, Management Science. --- Innovation/Technology Management. --- Administration --- Industrial relations --- Organization --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Calculus of variations. --- Decision making. --- Management science. --- Industrial management. --- Business administration --- Business enterprises --- Business management --- Corporate management --- Corporations --- Industrial administration --- Management, Industrial --- Rationalization of industry --- Scientific management --- Management --- Business --- Industrial organization --- Quantitative business analysis --- Problem solving --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Isoperimetrical problems --- Variations, Calculus of --- Engineering --- Engineering analysis --- Decision making --- Mathematics