On Functions and Functional Equations

Author: Smital

Publisher: CRC Press

ISBN: 9780852744185

Category: Mathematics

Page: 164

View: 9935

On Functions and Functional Equations introduces the main topics in iteration theory and the theory of functional equations with emphasis on applications in the fields of mathematics, physics, biology, chemistry, and electronics and mechanical engineering. The book contains many classical results as well as important, more recent results. It also includes numerous exercise and some problems that have yet to be resolved. The book is accessible to readers having a secondary level mathematical education.

Introduction to Functional Equations

Theory and Problem-solving Strategies for Mathematical Competitions and Beyond

Author: Costas Efthimiou

Publisher: American Mathematical Soc.

ISBN: 0821853147

Category: Mathematics

Page: 363

View: 4663

Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Functional Equations and Modelling in Science and Engineering

Author: Enrique Castillo

Publisher: CRC Press

ISBN: 9780824787172

Category: Mathematics

Page: 352

View: 2892

Provides engineers and applied scientists with some selected results of functional equations and their applications, with the intention of changing the way they think about mathematical modelling. Many of the proofs are simplified or omitted, so as not to bore or confuse engineers. Functional equati

Lectures on Functional Equations and Their Applications

Author: J. Aczel,Hansjorg Oser

Publisher: Courier Corporation

ISBN: 0486445232

Category: Mathematics

Page: 510

View: 2634

Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

Functional Equations in Applied Sciences

Author: Enrique Castillo,Andres Iglesias,Reyes Ruiz-Cobo

Publisher: Elsevier

ISBN: 9780080477916

Category: Mathematics

Page: 408

View: 3826

The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved. A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems. An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm. The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications. · A general methodology for solving functional equations is provided in Chapter 2. · It deals with functional networks, a powerful generalization of neural networks. · Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, illustrate the concept of functional equation. · Functional equations are presented as a powerful alternative to differential equations. · The book contains end of chapter exercises.

Functional Equations and Inequalities

Author: Themistocles RASSIAS

Publisher: Springer Science & Business Media

ISBN: 9401143412

Category: Mathematics

Page: 336

View: 1435

This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition of trigonometric functions, the functional equation of the square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution of zeros and inequalities for zeros of algebraic polynomials, a qualitative study of Lobachevsky's complex functional equation, functional inequalities in special classes of functions, replicativity and function spaces, normal distributions, some difference equations, finite sums, decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problems of expressibility in some extensions of free groups, Aleksandrov problem and mappings which preserve distances, Ulam's problem, stability of some functional equation for generalized trigonometric functions, Hyers-Ulam stability of Hosszú's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. Audience: This book will be of interest to mathematicians and graduate students whose work involves real functions, functions of a complex variable, functional analysis, integral transforms, and operational calculus.

Functional Equations and Inequalities in Several Variables

Author: Stefan Czerwik

Publisher: World Scientific

ISBN: 9789810248376

Category: Mathematics

Page: 410

View: 5638

This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with ? for the first time in the mathematical literature. The book contains many fresh results concerning those problems.

Functional Equations and Inequalities with Applications

Author: Palaniappan Kannappan

Publisher: Springer Science & Business Media

ISBN: 0387894926

Category: Mathematics

Page: 810

View: 2239

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.

Almost-Periodic Functions and Functional Equations

Author: L. Amerio,G. Prouse

Publisher: Springer Science & Business Media

ISBN: 1475712545

Category: Mathematics

Page: 184

View: 3009

The theory of almost-periodic functions with complex values, created by H. Bohr [1] in his two classical papers published in Acta Mathematica in 1925 and 1926, has been developed by many authors and has had note worthy applications: we recall the works of Weyl, De la Vallee Poussin, Bochner, Stepanov, Wiener, Besicovic, Favard, Delsarte, Maak, Bogoliu bov, Levitan. This subject has been widely treated in the monographs by Bohr [2], Favard [1], Besicovic [1], Maak [1], Levitan [1], Cinquini [1], Corduneanu [1], [2]. An important class of almost-periodic functions was studied at the beginning of the century by Bohl and Esclangon. Bohr's theory has been extended by Muckenhoupt [1] in a particular case and, subsequently, by Bochner [1] and by Bochner and Von Neumann [1] to very general abstract spaces. The extension to Banach spaces is, in particular, of great interest, in view of the fundamental importance of these spaces in theory and application.

Functional Equations on Groups

Author: Henrik Stetkær

Publisher: World Scientific

ISBN: 9814513148

Category: Mathematics

Page: 396

View: 932

This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, ℝ). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations. Contents:IntroductionAround the Additive Cauchy EquationThe Multiplicative Cauchy EquationAddition and Subtraction FormulasLevi–Civita's Functional EquationThe Symmetrized Sine Addition FormulaEquations with Symmetric Right Hand SideThe Pre-d'Alembert Functional EquationD'Alembert's Functional EquationD'Alembert's Long Functional EquationWilson's Functional EquationJensen's Functional EquationThe Quadratic Functional EquationK-Spherical FunctionsThe Sine Functional EquationThe Cocycle EquationAppendices:Basic Terminology and ResultsSubstitutes for CommutativityThe Casorati DeterminantRegularityMatrix-Coefficients of RepresentationsThe Small Dimension LemmaGroup Cohomology Readership: Advanced undergraduates, graduates and professional mathematicians interested in harmonic analysis and/or functional equations. Keywords:Functional Equation;Group;Harmonic AnalysisKey Features:Most of the material of the book can be found only in research papers, so it is a good source of referenceThe book is self-contained and provides the necessary background material needed to go further into the subject and to explore the research literatureThe book may be used as a textbook for graduate students and even ambitious undergraduate in mathematics, because it presents the material in an accessible way, originating from a course for students at master's levelExercises at the end of each chapter, some with answers, help to provide more examples to enable the student to grasp the topic betterReviews: “It is an excellent, well composed and self-contained monograph, written in good and clear English. It can serve as a complete and independent introduction to the field of trigonometric functional equations and as an excellent source of suitable references for further study. The scope of solutions considered extends from real functions to those acting between groups, also non-abelian.” Prof Janusz Brzdęk Pedagogical University Kraków, Poland “The book is written as an accessible introduction to trigonometric functional equations for graduate students and working mathematicians. It gives a very readable account of recent research in the area, as well as more than 200 references for further study. It would make an excellent textbook for a graduate course on the topic. This monograph is a valuable contribution to the literature on functional equations.” Zentralblatt MATH

Mean Value Theorems and Functional Equations

Author: P K Sahoo,T Riedel

Publisher: World Scientific

ISBN: 9814495875

Category: Mathematics

Page: 260

View: 4331

This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed. Contents:Additive and Biadditive FunctionsLagrange's Mean Value Theorem and Related Functional EquationsPompeiu's Mean Value Theorem and Associated Functional EquationsTwo-Dimensional Mean Value Theorems and Functional EquationsSome Generalizations of Lagrange's Mean Value TheoremMean Value Theorems for Some Generalized DerivativesSome Integral Mean Value Theorems and Related Topics Readership: Pure mathematicians. Keywords:Functional Equations;Integral Mean Value Theorem;Cauchy Mean Value Theorem;Inequalities;Mean Values;Textbook;Pompeiu Mean Value Theorem;Flett Mean Value Theorem;Trahan Mean Value Theorem;Differential Mean Value Theorem;Lagrange Mean Value Theorem

Iterative Functional Equations

Author: Marek Kuczma,Bogdan Choczewski,Roman Ger

Publisher: Cambridge University Press

ISBN: 9780521355612

Category: Mathematics

Page: 552

View: 3424

A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.

Functional Equations in Several Variables

Author: J. Aczel,Jean G. Dhombres

Publisher: Cambridge University Press

ISBN: 9780521352765

Category: Mathematics

Page: 462

View: 9939

Deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioral, and social sciences. The authors emphasize applications, although not at the expense of theory, and have kept the prerequisites to a minimum; the reader should be familiar with calculus and some simple structures of algebra and have a basic knowledge of Lebesque integration. For the applications the authors have included references and explained the results used. The book is designed so that the chapters may be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. Each chapter concludes with exercises and further results, 400 in all, which extend and test the material presented in the text. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography of over 1600 items. This volume will be of interest to professionals and graduate students in pure and applied mathematics.

Handbook of Functional Equations

Functional Inequalities

Author: Themistocles M. Rassias

Publisher: Springer

ISBN: 1493912461

Category: Mathematics

Page: 555

View: 4708

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Volterra Integral and Functional Equations

Author: G. Gripenberg,S. O. Londen,O. Staffans

Publisher: Cambridge University Press

ISBN: 9780521372893

Category: Mathematics

Page: 701

View: 4213

This book looks at the theories of Volterra integral and functional equations.

Convolution Type Functional Equations on Topological Abelian Groups

Author: L szl¢ Sz‚kelyhidi

Publisher: World Scientific

ISBN: 9789810206581

Category: Mathematics

Page: 157

View: 6319

This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results.

Functional Equations — Results and Advances

Author: Zoltan Daroczy,Zsolt Páles

Publisher: Springer Science & Business Media

ISBN: 1475752881

Category: Mathematics

Page: 361

View: 689

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. First of all, this is due to the fact that the mathematical applications raised the investigations of newer and newer types of functional equations. At the same time, the self development of this theory was also very fruitful. This can be followed in many monographs that treat and discuss the various methods and approaches. These developments were also essentially influenced by a number jour nals, for instance, by the Publicationes Mathematicae Debrecen (founded in 1953) and by the Aequationes Mathematicae (founded in 1968), be cause these journals published papers from the field of functional equa tions readily and frequently. The latter journal also publishes the yearly report of the International Symposia on Functional Equations and a comprehensive bibliography of the most recent papers. At the same time, there are periodically and traditionally organized conferences in Poland and in Hungary devoted to functional equations and inequali ties. In 2000, the 38th International Symposium on Functional Equations was organized by the Institute of Mathematics and Informatics of the University of Debrecen in Noszvaj, Hungary. The report about this meeting can be found in Aequationes Math. 61 (2001), 281-320.

Functional Equations and Characterization Problems on Locally Compact Abelian Groups

Author: Gennadiĭ Mikhaĭlovich Felʹdman

Publisher: European Mathematical Society

ISBN: 9783037190456

Category: Mathematics

Page: 256

View: 7485

This book deals with the characterization of probability distributions. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analyses, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory.

Functional Equations

Author: David Leigh-Lancaster

Publisher: Aust Council for Ed Research

ISBN: 0864314922

Category: Education

Page: 114

View: 6325

Functional equations provides mathematics teachers with an introduction to elementary aspects of functional equations. These equations are linked to function in various topics of the senior secondary mathematics curriculum including transformations, identities difference equations and mathematical modelling.

On Applications and Theory of Functional Equations

Author: J. Aczél

Publisher: Academic Press

ISBN: 1483262650

Category: Mathematics

Page: 64

View: 7437

On Applications and Theory of Functional Equations focuses on the principles and advancement of numerical approaches used in functional equations. The publication first offers information on the history of functional equations, noting that the research on functional equations originated in problems related to applied mathematics. The text also highlights the influence of J. d'Alembert, S. D. Poisson, E. Picard, and A. L. Cauchy in promoting the processes of numerical analyses involving functional equations. The role of vectors in solving functional equations is also noted. The book ponders on the international Fifth Annual Meeting on Functional Equations, held in Waterloo, Ontario, Canada on April 24-30, 1967. The meeting gathered participants from America, Asia, Australia, and Europe. One of the topics presented at the meeting focuses on the survey of materials dealing with the progress of approaches in the processes and methodologies involved in solving problems dealing with functional equations. The influence, works, and contributions of A. L. Cauchy, G. Darboux, and G. S. Young to the field are also underscored. The publication is a valuable reference for readers interested in functional equations.