3
votes
3answers
161 views

$1992$ IMO Functional Equation problem

The problem states: Let $\Bbb R$ denote the set of all real numbers. Find all functions $f : \Bbb R \rightarrow \Bbb R$ such that $$f(x^{2}+f(y))=y+(f(x))^{2} \space \space \space \forall x, y \in ...
0
votes
0answers
33 views

General solution of the recurrence equation with real shifts

How to find a general solution of the following functional (recurrence) equation: $$f(x) = c_1 f(x - a_1) + \dots + c_n f(x - a_n), \tag{1}$$ where $c_i, a_i$, $i = 1, ... n$ are arbitrary real ...
1
vote
1answer
55 views

Reference request: Where is this functional equation found?

$$ g\left(\frac{x+y}{1+xy}\right) = g(x)g(y). $$ One solution is $$ g(x) = \frac{1+x}{1-x}. $$ Another is $$ g(x) = \sqrt\frac{1+x}{1-x}. $$ Any other power of the first solution is also a solution, ...
2
votes
1answer
356 views

Functional equation book for olympiad

what may be the good suggestions in olympiad functional equations for a beginner for . I have heard of this book by B.J.Venkatachala but do not whether it will be suitable for me or not. Anybody ...
10
votes
2answers
275 views

When is $f^{-1}=1/f\,$?

I seem to remember a nice article that I read many years ago (perhaps in the American Mathematical Monthly) which investigated the question, "Under what conditions on $f:\mathbb{C}\to\mathbb{C}$ is ...
1
vote
1answer
175 views

Books on functional equations

Could you help me please with some functional equations? I need some online books with exercises and some explanations. I'm interested in the Cauchy functional equation and Jensen functional equation. ...
-3
votes
1answer
171 views

What is a good list of more than 20 math books for functional equation with 200+ pages of each [closed]

What is your good list of more than 20 math books for functional equation with 200+ pages of each? And not very specific book with very complicated/very sophiscated topic for mathmatician please! It ...
2
votes
2answers
297 views

Correct order of books for a beginner

what should be the order of the books in which a beginner should do the following books in algebra: -1.E.J. Barbeau POLYNOMIALS -2. Polynomials and Polynomial Inequalities (Graduate Texts in ...
2
votes
2answers
194 views

Recurrence relations on a continuous domain

While attempting to read Shannon's paper I came across the following (p. 3): suppose $N\colon \mathbb{R} \to \mathbb{R}$ is a function, which for some fixed (given) set of values $t_1, t_2, \dots, ...
3
votes
1answer
152 views

Starting out with functional equations

I am thinking of starting learning about various functional equations and ways to solve them, any help as to which books could be of help to me? I have some knowledge about some basic functional ...
3
votes
0answers
77 views

Function Shape Reference

I'm wondering if their exists a visual/behavioral reference for the fundamental families of functions. I'm not a mathematician so excuse my language if I'm being overly vague. I would like to have a ...