Difference between operator() and operator>>?

I am just playing with std::function<> and operators, just to make C++ statements look like Functional Languages(F#) and found out that there is a difference between operator() and operator<<. My code :

Function 1 (Operator Overload):

function<int(int)> operator>>(function<int(int)> f1, function<int(int)> f2)
{
  function<int(int)> f3 = [=](int x){return f1(f2(x));};
  return f3;
}

Function 2 (Operator Overload):

function<int(int, int)> operator>>(function<int(int, int)> f1, function<int(int)> f2)
{
  function<int(int, int)> f3 = [=](int x,int y){return f2(f1(x, y));};
  return f3;
}

Function 3 (Operator Overload):

function<int(int)> operator()(function<int(int, int)> f1, int x)
{
  function<int(int)> f2 = [=](int y){return f1(x, y);};
  return f2;
}

while the Function 1 and Function 2 ( or Operator Overload ), Function 3 gives out error that :

error: β€˜std::function<int(int)> operator()(std::function<int(int, int)>, int)’ must be a nonstatic member function
     function<int(int)> operator()(function<int(int, int)> f1, int x)
                                                                    ^

Why do operator() needs to be non-static member?
I think its different than What is the difference between the dot (.) operator and -> in C++? In that question the answer is explained in terms of pointers. But here I am using simple operator() and operator>>, which has nothing to do with pointers.


Source: gcc

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