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Using the {\it nonlinear coherent states method}, a formalism for theconstruction of the coherent states associated to {\it "inverse bosonicoperators"} and their dual family has been proposed. Generalizing the approach,the "inverse of $f$-deformed ladder operators" corresponding to the nonlinearcoherent states in the context of quantum optics and the associated coherentstates have been introduced. Finally, after applying the proposal to a fewknown physical systems, particular nonclassical features as sub-Poissonianstatistics and the squeezing of the quadratures of the radiation fieldcorresponding to the introduced states have been investigated.

New nonlinear coherent states associated to inverse bosonic and $f$-deformed ladder operators