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Note that any igeneigen-function satisfies youyour condition for some $C>0$.
It remains to find a non-symmetric one. Take for example
$$f(x,y,z)=10\cdot x^3+y^3+\tfrac1{10}\cdot z^3.$$
Note that any igen-function satisfies you condition for some $C>0$.
It remains to find a non-symmetric one. Take for example
$$f(x,y,z)=10\cdot x^3+y^3+\tfrac1{10}\cdot z^3.$$
Note that any eigen-function satisfies your condition for some $C>0$.
It remains to find a non-symmetric one. Take for example
$$f(x,y,z)=10\cdot x^3+y^3+\tfrac1{10}\cdot z^3.$$
Note that any igen-function satisfies you condition for some $C>0$.
It remains to find a non-symmetric one, which seems to be easy. Take for example
$$f(x,y,z)=10\cdot x^3+y^3+\tfrac1{10}\cdot z^3.$$
Note that any igen-function satisfies you condition for some $C>0$.
It remains to find a non-symmetric one, which seems to be easy.
Note that any igen-function satisfies you condition for some $C>0$.
It remains to find a non-symmetric one. Take for example
$$f(x,y,z)=10\cdot x^3+y^3+\tfrac1{10}\cdot z^3.$$
