The main aim of this paper is to present the concept of general Mann type doubly sequence iteration process with errors to approximate fixed points. We prove that the general Mann type doubly sequence iteration process with errors converges strongly to a coincideness point of two continuous pseudo-contractive mappings both of them which maps a bounded closed convex nonempty subset of a real Hilbert space into itself. Moreover, we discuss equivalence from the S,T-stability point of view under certain restrictions between general Mann type doubly sequence iteration process with errors and general Ishikawa iterations with errors. An application is also given to support our idea using compatible-type of mappings.