Within the area of hyperspectral data processing, nonlinear unmixing techniques have emerged as promising alternatives for overcoming the limitations of linear methods. In this paper, we consider the class of post-nonlinear mixing models of the partially linear form. More precisely, these composite models consist of a linear mixing part and a nonlinear fluctuation term defined in a reproducing kernel Hilbert space, both terms being parameterized by the endmember spectral signatures and their respective abundances. These models consider that the reproducing kernel may also depend advantageously on the fractional abundances. An iterative algorithm is then derived to jointly estimate the fractional abundances and to infer the nonlinear functional term.