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