Is there any example, or theorem, or know-how on this problem?
f(x1,x2...xm, k, n): Z1 x Z2 x...x Zm x N x N* -> R,
with form:
f(x1,x2...xm, k, n)=k-root[(x1^k+x2^k+...+xm^k)/n],
where: k-root[...] is the k-th root of [...]. Not k minus SQR[...] !
Equally important here are the surjectivity on R and its form.
P.S. of course I do not mind if the answer is available only for the "trivial" Pithagora cases: k=2 and n=1.
Same, if the answer comes from any of mathematics specialty.
This is no home-work of any kind. It is simply a long time present curiosity.
Thank you all for any (relevant) answers.
f(x1,x2...xm, k, n): Z1 x Z2 x...x Zm x N x N* -> R,
with form:
f(x1,x2...xm, k, n)=k-root[(x1^k+x2^k+...+xm^k)/n],
where: k-root[...] is the k-th root of [...]. Not k minus SQR[...] !
Equally important here are the surjectivity on R and its form.
P.S. of course I do not mind if the answer is available only for the "trivial" Pithagora cases: k=2 and n=1.
Same, if the answer comes from any of mathematics specialty.
This is no home-work of any kind. It is simply a long time present curiosity.
Thank you all for any (relevant) answers.