In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to "heavy" string states, while the third vertex corresponds to a "light" state. This is done for the case when the "heavy" string states are finite-size giant magnons, carrying one or two angular momenta. The "light" states are taken to be singlet scalar operators on higher string levels. We first consider the case of

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... ing theory on AdS_5xS^5 dual to N = 4 super Yang-Mills. Then we extend the obtained results to the gamma-deformed AdS_5x S^5, corresponding to N = 1 super Yang-Mills theory, appearing as an exactly marginal deformation of N=4 super Yang-Mills.