Bulletin of the
Korean Mathematical Society BKMS

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized $\Phi$-contractive conditions in Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

Keywords: t-norm, non-Archimedean Menger PM-space, weakly compatible mappings, common limit range property, fixed point

MSC numbers: 47H10, 54H25