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Functional Equations
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- Enrique Castillo 2 ,
- Angel Cobo 2 ,
- José Manuel Gutiérrez 2 &
- Rosa Eva Pruneda 2
Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 473))
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The importance of functional equations is comparable to that of differential equations because many of the problems that can be stated in terms of a differential equation or a system of differential equations can also be stated in terms of a functional equation or a system of functional equations. However, functional equations are easier and more natural than differential equations because they do not involve derivatives.
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Dpto.de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain
Enrique Castillo, Angel Cobo, José Manuel Gutiérrez & Rosa Eva Pruneda
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Castillo, E., Cobo, A., Gutiérrez, J.M., Pruneda, R.E. (1999). Functional Equations. In: Functional Networks with Applications. The Springer International Series in Engineering and Computer Science, vol 473. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5601-5_3
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Functional Equations in Mathematical Olympiads (2017 - 2018): Problems and Solutions (Vol. I)
2018, Independently published
Functional equations, which are a branch of algebraic problems used in mathematical competitions, appear in recent olympiads very frequently. The current book is the first volume in a series of books on collections of solved problems in functional equations. This volume contains 175 problems on the subject, including those used in latest mathematical olympiads (2017 - 2018) around the world. The basic concepts of functional equations and techniques of problem solving have been briefly discussed in the preamble of the book.
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A functional equation is an equation where the unknown is a function rather than a variable. It may happen that one knows only a certain property of a function; e.g. that it is even, i.e., f (x) = f (–x) for all x; or that it is additive, i.e., f (x + y) = f (x) + f (y) for all x, y; and so on. The question that then arises is, what functions exist with the stated property? Is there just one such function? In this two-part article, we answer such questions for certain types of functional equations. Functional equations are used to model behaviour in engineering fields (e.g., Shannon's entropy in Information Theory) and the social sciences. They are also of use in the study of difference equations
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The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Székelyhidi’s result may be generalized to equations where some occurrences of the unknown functions are multiplied by a linear combination of the variables. In this paper we study the equations where two such combinations appear. The simplest nontrivial example of such a case is given by the equation $$\begin{aligned} F(x + y) - F(x) - F(y) = yf(x) + xf(y) \end{aligned}$$ F ( x + y ) - F ( x ) - F ( y ) = y f ( x ) + x f ( y ) considered by Fechner and Gselmann (Publ Math Debrecen 80(1–2):143–154, 2012). In the present paper we prove several results concerning the systematic approach to the generalizations of this equation.
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Functional Equations A Problem Solving Approach. B. J. Venkatachala. Prism, 2002 - 218 pages. Bibliographic information. Title: Functional Equations A Problem Solving Approach: ... Functional Equations A Problem Solving Approach. B. J. Venkatachala. Prism, 2002 - 218 pages. Bibliographic information. Title: Functional Equations A Problem ...
Functional Equations a Problem Solving Approach by b j Venkatachala z Liborg Pr 6c1230f9a977d9a3d891344de1a9ae12 - Free ebook download as PDF File (.pdf) or read book ...
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 ...
§3Cauchy's Functional Equation Over Q For this section, all functions are f : Q !Q. We highly encourage the reader to try these examples on their own before reading the solutions; they are good practice problems! Example 3.1 (Cauchy's Functional Equation) Solve f(x+ y) = f(x) + f(y) over Q. Solution.
Functional Equations A Problem Solving Approach by B. J. Venkatachala (z-lib.org).pdf - Free ebook download as PDF File (.pdf) or read book online for free. Scribd is the world's largest social reading and publishing site.
Functional Equations a Problem Solving Approach by B. J. Venkatachala (Z-lib.org) - Free ebook download as PDF File (.pdf) or read book online for free. Scribd is the world's largest social reading and publishing site. ...
f(x + f(y)) + f(xy) = f(x + 1)f(y + 1) 1. (again I made that up). This equation is "almost symmetric", except for a "bump" on the far left where f(x + f(y)) is asymmetric. So if we take the equation with x and y flipped and then eliminate the common terms, we manage to obtain. f(x + f(y)) = f(y + f(x)):
Download PDF - Functional Equations A Problem Solving Approach By B. J. Venkatachala (z-lib.org).pdf [x25d5575q9wp]. - Revised & and — Updated a Functional Equations A Problem Solving Approach Problems from Mathematical Olympiads and oth...
Loading documents preview... Download & View as PDF for free. Related Documents. Functional Equations A Problem Solving Approach By B. J. Venkatachala (z-lib.org).pdf. January 20211. Geotechnical Engineering- A Practical Problem Solving Approach. February 20211. Functional Equations.. January 20211.
Download chapter PDF An historical introduction. Pages 1-29. Download ... a number of books have been written on the theory of functional equations. However, very little has been published which helps readers to solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap.
1.Functional equations with integers, where you use the fact that the integers are discrete. 2.Functional equations over R where you use algebraic manipulations. 3.Functional equations over R where you use analytic properties of f(x), such that continuity or di er-entiability or integrability. 2 Problems 2.1 Functional equations and the ...
Example 1.1 The following equations can be regarded as functional equations f(x) = f(x); odd function f(x) = f(x); even function f(x + a) = f(x); periodic function, if a , 0 Example 1.2 The Fibonacci sequence a n+1 = a n + a n1 defines a functional equation with the domain of which being nonnegative integers. We can also represent the sequence ...
Functional Equations - A Problem Solving Approach (Revised and Updated 2nd ED) In stock. SKU. PBK0000342. ISBN10: 8172867816: ISBN13: 9788172867812: Binding: ... Country of Origin: India ₹350.00 298.00. Qty; ADD TO CART; Share Functional Equations - A Problem Solving Approach (Revised and Updated 2nd ED) on. Well done! You successfully read ...
a formal definition of a functional equation and give the general solutions of the most important functional equations to be used in the remaining parts of this book. Vie also give the corresponding uniqueness theorems. In Section 3.4 we give general methods to solve functional equations, illus trating them with simple examples.
The basic concepts of functional equations and techniques of problem solving have been briefly discussed in the preamble of the book. See Full PDF Download PDF. See Full PDF Download PDF. Related Papers. ... My initial goal for creating a problem set in functional equations was to publish a book of over 3000 questions solved by the user pco in ...
Functional_Equations_A_Problem_Solving.pdf - Free ebook download as PDF File (.pdf) or read book online for free. Scribd is the world's largest social reading and publishing site.
1 Definitions • N is the set of positive integers. • N ∪{0} = N∗ is the set of non-negative integers. • Z is the set of integers. • Q is the set of rational numbers. • R+ is the set of positive real numbers. • R is the set of real numbers.
A classic example of such a function is because . Cyclic functions can significantly help in solving functional identities. Consider this problem: Find such that . In this functional equation, let and let . This yields two new equations: Now, if we multiply the first equation by 3 and the second equation by 4, and add the two equations, we have:
Functional equations are often the most difficult problems to be found on mathematics competitions because they require a minimal amount of background theory and a maximal amount of ingenuity. The great advantage of a problem involv-ing functional equations is that you can construct problems that students at all levels can understand and play with.
19.Find all strictly monotone functions f: R !R satisfying the functional equation f(f(x) + y) = f(x+ y) + f(0) for all x;y 2R. 20.Find all continous functions f: R !R 0 such that f(x+ y) = f(x) + f(y) + f(x)f(y) for all x;y 2R. References [1]B. J. Venkatachala, Functional Equations: A Problem Solving Approach, Prism Books Pvt. Ltd., 2002
Created Date: 9/26/2011 1:16:37 PM
This paper investigates a novel C0 nonconforming virtual element method (VEM) for solving the Kirchhoff plate obstacle problem, which is described by a fourth-order variational inequality (VI) of the first kind. In our study, we distinguish our approach by introducing new internal degrees of freedom to the traditional lowest-order C0 nonconforming VEM, which originally lacked such degrees ...