Advanced Fixed Point Theory For Economics
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Advanced Fixed Point Theory For Economics
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Author : Andrew McLennan
language : en
Publisher: Springer
Release Date : 2018-07-03
Advanced Fixed Point Theory For Economics written by Andrew McLennan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Business & Economics categories.
This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstandingtext for advanced graduate courses in economics and related disciplines.
Fixed Point Theory In P Vector Spaces
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Author : George Xianzhi Yuan
language : en
Publisher: World Scientific
Release Date : 2025-05-05
Fixed Point Theory In P Vector Spaces written by George Xianzhi Yuan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.
This monograph provides an updated development of fixed point theory under a unified framework of the 'best approximation approach' in p-vector spaces, a core component of nonlinear analysis in mathematics, where p∊(0,1] (the same for p below unless specified). This book exposes some important contents of the new fixed point theory, with highlights in four parts.Specifically, the book focuses on the development of general new fixed point theory for both single-valued and set-valued mappings under the framework of p-vector and locally convex spaces for p∊(0,1], including topological vector spaces and locally convex spaces as special cases. It provides affirmative answers to the Schauder conjecture under the general setting of p-vector spaces and locally p-convex spaces. The book establishes best approximation results for upper semicontinuous and 1-set contractive set-valued mappings, which are used as tools to establish new fixed point theorems for non-self set-valued mappings with either inward or outward set conditions under various situations. These results improve or unify corresponding results in the existing literature for nonlinear analysis and lay the foundation for the development of fixed point theorems in topological vector spaces since Schauder's conjecture was raised in 1930. In addition, this book demonstrates the power of the fixed point theorem by showing the equivalence among the Ekeland variational principle, Takahashi minimization theorem, Oettli-Théra theorem, Caristi-Kirk type fixed point theorem, and related principles in nonlinear functional analysis.Overall, this book provides an accessible way to establish the new theory in the development of fixed point theorems and results. It is designed to be understandable for senior undergraduate students majoring in mathematics, physical sciences, social sciences, and related fields. We expect that this monograph will serve as a staple textbook for undergraduate and postgraduate students, a reference book for researchers in the field of fixed point theory in nonlinear functional analysis, and an accessible resource for general readers in mathematics and related disciplines.
Alternative Approaches To Economic Theory
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Author : Victor A. Beker
language : en
Publisher: Routledge
Release Date : 2019-06-11
Alternative Approaches To Economic Theory written by Victor A. Beker and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Business & Economics categories.
The 2007–2008 financial crisis exposed the shortcomings of mainstream economic theory with economists unprepared to deal with it. In the face of this, a major rethinking of economics seems necessary and in presenting alternative approaches to economic theory, this book contributes to the rebuilding of the discipline. This volume brings together contributions from different perspectives and theoretical approaches that address the challenge of updating the economic theory corpus and seek to recover prestige for this discipline after the failure of neoclassical economics. It addresses a range of topics, including the complexity approach to economics, category theory, the Post-Keynesian approach to micro and macroeconomics, financialisation, multidimensional analysis and ecological economics. The book is aimed at economics scholars, researchers, academics and practitioners, as well as upper undergraduates and graduates in this area of knowledge. It may also be of interest for people interested in methodological issues in economics and the relationship between economic theory and the real world.
Handbook Of Game Theory And Industrial Organization Volume I
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Author : Luis C. Corchón
language : en
Publisher: Edward Elgar Publishing
Release Date : 2018-02-23
Handbook Of Game Theory And Industrial Organization Volume I written by Luis C. Corchón and has been published by Edward Elgar Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Business & Economics categories.
The first volume of this wide-ranging Handbook contains original contributions by world-class specialists. It provides up-to-date surveys of the main game-theoretic tools commonly used to model industrial organization topics. The Handbook covers numerous subjects in detail including, among others, the tools of lattice programming, supermodular and aggregative games, monopolistic competition, horizontal and vertically differentiated good models, dynamic and Stackelberg games, entry games, evolutionary games with adaptive players, asymmetric information, moral hazard, learning and information sharing models.
Mathematical Economics
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Author : Kam Yu
language : en
Publisher: Springer Nature
Release Date : 2019-11-01
Mathematical Economics written by Kam Yu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-01 with Mathematics categories.
This textbook provides a one-semester introduction to mathematical economics for first year graduate and senior undergraduate students. Intended to fill the gap between typical liberal arts curriculum and the rigorous mathematical modeling of graduate study in economics, this text provides a concise introduction to the mathematics needed for core microeconomics, macroeconomics, and econometrics courses. Chapters 1 through 5 builds students’ skills in formal proof, axiomatic treatment of linear algebra, and elementary vector differentiation. Chapters 6 and 7 present the basic tools needed for microeconomic analysis. Chapter 8 provides a quick introduction to (or review of) probability theory. Chapter 9 introduces dynamic modeling, applicable in advanced macroeconomics courses. The materials assume prerequisites in undergraduate calculus and linear algebra. Each chapter includes in-text exercises and a solutions manual, making this text ideal for self-study.
Fixed Point Theorems With Applications To Economics And Game Theory
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Author : Kim C. Border
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-16
Fixed Point Theorems With Applications To Economics And Game Theory written by Kim C. Border and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-16 with Business & Economics categories.
One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students.
Brouwer Degree
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Author : George Dinca
language : en
Publisher: Springer Nature
Release Date : 2021-05-11
Brouwer Degree written by George Dinca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-11 with Mathematics categories.
This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.
Metric Fixed Point Theory
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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-01-04
Metric Fixed Point Theory written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Mathematics categories.
This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.
Real Analysis With Economic Applications
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Author : Efe A. Ok
language : en
Publisher: Princeton University Press
Release Date : 2011-09-05
Real Analysis With Economic Applications written by Efe A. Ok and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-05 with Business & Economics categories.
There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.
Computable Foundations For Economics
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Author : K. Vela Velupillai
language : en
Publisher: Routledge
Release Date : 2012-07-26
Computable Foundations For Economics written by K. Vela Velupillai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-26 with Business & Economics categories.
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.