Document Type : Research Paper

Author

• M. Akkouchi

Department of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Av. Prince My. Abdellah, P. O. Box, 2390, Marrakech, Morocco (Maroc).

Abstract

In this paper, we introduce the concept of generalized $\varphi$-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 $\varphi$-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 by Qingnian Zhang and Yisheng Song.

Keywords

• Common fixed point for four mappings
• generalized $phi$−contractions
• lower semi-continuity
• weakly compatible mappings
• well-posed common fixed point problem