Common fixed point theorems of compatible and weakly compatible maps in Menger spaces

Abstract

In this paper, we prove some new common fixed point theorems for compatible and weakly compatible self-maps on Menger space under ϕ -contractive conditions. Our results improve and generalize the results of Singh and Jain [B. Singh, S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2005) 439–448], Razani and Shirdaryazdi [A. Razani, M. Shirdaryazdi, A common fixed point theorem of compatible maps in Menger space, Chaos Solitons Fractals 32 (2007) 26–34] and others.