Question

Difficulty with Jensen's Equation.

score 655 · Answer 1 · 2015-01-25 16:13:31

655

Views

Difficulty with Jensen's Equation.

Published on 25 Jan 2015 - 16:13

score 899 · Answer 2 · 2015-01-27 17:55:17

899

Views

Fixed Point Iteration $x = g(x)$ method for $y_1 = e ^{-x}$ and $y_2= \cos x$

Published on 27 Jan 2015 - 17:55

score 703 · Answer 3 · 2015-01-28 10:58:09

703

Views

For all $x,y\in G$ we have: $f(xf(y))=f(x)y$. Prove that $f$ is an isomorphism?

Published on 28 Jan 2015 - 10:58

score 109 · Answer 4 · 2015-01-28 14:49:03

109

Views

A functional equation problem over integers: $f(m+n)=g(m,n)+h(m,n)$ and $f(m-n)=g(m,n)-h(m,n)$

Published on 28 Jan 2015 - 14:49

score 234 · Answer 5 · 2015-01-28 17:04:43

234

Views

Calculation of Sigma (Multiple Sigmas)

Published on 28 Jan 2015 - 17:04

score 1.2k · Answer 6 · 2015-01-28 19:09:08

1.2k

Views

Improvement IMO 1988 $f(f(n))=n+1987$

Published on 28 Jan 2015 - 19:09

score 80 · Answer 7 · 2015-01-29 14:31:10

80

Views

Solution techniques for f'(x)=f(g(x))

Published on 29 Jan 2015 - 14:31

score 740 · Answer 8 · 2015-01-29 21:55:32

740

Views

Solving functional equation $f(x)f(y) = f(x+y)$

Published on 29 Jan 2015 - 21:55

score 72 · Answer 9 · 2015-01-31 11:02:10

72

Views

Solving for this function

Published on 31 Jan 2015 - 11:02

score 128 · Answer 10 · 2015-01-31 19:16:42

128

Views

$f(xy)=\frac{f(x)+f(y)}{x+y}$ Prove that $f$ is identically equal to $0$

Published on 31 Jan 2015 - 19:16

score 1.9k · Answer 11 · 2015-02-01 16:01:43

1.9k

Views

Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$

Published on 01 Feb 2015 - 16:01

score 148 · Answer 12 · 2015-02-02 16:23:51

148

Views

Functional equation defined over non-negative real numbers: $f^{-1}\big(f(x)f(y)\big)=\frac{f(x+y)-f(x)-f(y)}2$

Published on 02 Feb 2015 - 16:23

score 1.5k · Answer 13 · 2015-02-04 15:43:05

1.5k

Views

Find all real functions $f:\mathbb {R} \to \mathbb {R}$ satisfying the equation $f(x^2+y.f(x))=x.f(x+y)$

Published on 04 Feb 2015 - 15:43

score 58 · Answer 14 · 2015-02-05 09:50:25

58

Views

Technique to iterative functional equations $f_{(r)}(x)=2^{(\log x)^c}$ and $g_{(r)}(x)=2^{x^\frac{1}{c}}$

Published on 05 Feb 2015 - 9:50

score 157 · Answer 15 · 2015-02-05 22:14:39

157

Views

Function preserving exponentiation

Published on 05 Feb 2015 - 22:14

List Question

Difficulty with Jensen's Equation.

Fixed Point Iteration $x = g(x)$ method for $y_1 = e ^{-x}$ and $y_2= \cos x$

For all $x,y\in G$ we have: $f(xf(y))=f(x)y$. Prove that $f$ is an isomorphism?

A functional equation problem over integers: $f(m+n)=g(m,n)+h(m,n)$ and $f(m-n)=g(m,n)-h(m,n)$

Calculation of Sigma (Multiple Sigmas)

Improvement IMO 1988 $f(f(n))=n+1987$

Solution techniques for f'(x)=f(g(x))

Solving functional equation $f(x)f(y) = f(x+y)$

Solving for this function

$f(xy)=\frac{f(x)+f(y)}{x+y}$ Prove that $f$ is identically equal to $0$

Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$

Functional equation defined over non-negative real numbers: $f^{-1}\big(f(x)f(y)\big)=\frac{f(x+y)-f(x)-f(y)}2$

Find all real functions $f:\mathbb {R} \to \mathbb {R}$ satisfying the equation $f(x^2+y.f(x))=x.f(x+y)$

Technique to iterative functional equations $f_{(r)}(x)=2^{(\log x)^c}$ and $g_{(r)}(x)=2^{x^\frac{1}{c}}$

Function preserving exponentiation

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