Department of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, P. O. Box, 2390, Marrakech, Morocco (Maroc).
In this paper, we introduce the concept of generalized -contractivity
of a pair of maps w.r.t. another pair. We establish a common fixed point result for
two pairs of self-mappings, when one of these pairs is generalized -contraction
w.r.t. the other and study the well-posedness of their fixed point problem. In
particular, our fixed point result extends the main result of a recent paper of
Qingnian Zhang and Yisheng Song.