Solving $f(x) = f(g(x)),h(x)$ for $f$
How do I go about solving equations of the form
$f(x) = f(g(x)),h(x)$
for the function f, given functions $g$ and $h$? Is there maybe some integral transform that I could use? When $h(x)$ is constant, then this would be Schröder's equation, but in my case $h(x)$ is not constant.
If this can be solved, how would you tackle the more complicated problem of solving
$f(x) = sum_i f(g_i(x)),h_i(x)$
for the function $f$, given the finite sets of functions ${g_i}$ and ${h_i}$?
functional-equations
asked Nov 23 at 13:24
JEM_Mosig
1236
add a comment |
How do I go about solving equations of the form
$f(x) = f(g(x)),h(x)$
for the function f, given functions $g$ and $h$? Is there maybe some integral transform that I could use? When $h(x)$ is constant, then this would be Schröder's equation, but in my case $h(x)$ is not constant.
If this can be solved, how would you tackle the more complicated problem of solving
$f(x) = sum_i f(g_i(x)),h_i(x)$
for the function $f$, given the finite sets of functions ${g_i}$ and ${h_i}$?
functional-equations
asked Nov 23 at 13:24
JEM_Mosig
1236
add a comment |
How do I go about solving equations of the form
$f(x) = f(g(x)),h(x)$
for the function f, given functions $g$ and $h$? Is there maybe some integral transform that I could use? When $h(x)$ is constant, then this would be Schröder's equation, but in my case $h(x)$ is not constant.
If this can be solved, how would you tackle the more complicated problem of solving
$f(x) = sum_i f(g_i(x)),h_i(x)$
for the function $f$, given the finite sets of functions ${g_i}$ and ${h_i}$?
functional-equations
asked Nov 23 at 13:24
JEM_Mosig
1236
How do I go about solving equations of the form
$f(x) = f(g(x)),h(x)$
for the function f, given functions $g$ and $h$? Is there maybe some integral transform that I could use? When $h(x)$ is constant, then this would be Schröder's equation, but in my case $h(x)$ is not constant.
If this can be solved, how would you tackle the more complicated problem of solving
$f(x) = sum_i f(g_i(x)),h_i(x)$
for the function $f$, given the finite sets of functions ${g_i}$ and ${h_i}$?
functional-equations
functional-equations
asked Nov 23 at 13:24
JEM_Mosig
1236
asked Nov 23 at 13:24
JEM_Mosig
1236
edited Nov 23 at 16:42
asked Nov 23 at 13:24
JEM_Mosig
1236
asked Nov 23 at 13:24
JEM_Mosig
1236
asked Nov 23 at 13:24
JEM_Mosig
1236
1236
add a comment |
add a comment |
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