Abstract: In view of the existence theory for fixed point of a continuous pseudocontractive mapping, a new composite implicit iterative process with errors for a finite family of strictly pseudocontractive mappings is introduced reasonably in a real smooth Banach space. We have proved by means of the Petryshyn’s inequality that the iterative process converges strongly to a fixed point of the family of strictly pseudocontractive mappings under some suitable conditions.

Key words: composite implicit iterative process, strictly pseudo contractive mappings, common fixed point