Inspired by the concept of integral type (Branciari type) contractive condition and respective fixed point results, we derive some new common fixed point theorems for quadruple self mappings satisfying a generalized W-contractive condition or a generalized w-contractive condition of integral type, also using the notions of compatibility and subsequential continuity (alternately subcompatibility and reciprocal continuity) in the frame of metric spaces. We furnish some examples to illustrate the useability of our main results. Several results existing in the literature are obtained as consequences of the main results. At the end of this article the existence and uniqueness of solutions for certain systems of integral equations and functional equations arising in dynamic programming are demonstrated with the help of the obtained results. © 2015 Miskolc University Press.