Photon-added coherent states as nonlinear coherent states

The states |α,m〉, defined as â†m|α〉 up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f(n̂,m)â where f(n̂,m) is a nonlinear function of the number operator n̂. The explicit form of f(n̂,m) is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of the state |α,m〉.