Common Fixed Point in Cone Metric Space for $mathbf{s}-mathbf{varphi}$-contractive

Abstract

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric space has been introduced. We have defined $s-phi$-contractive and obtained common fixed point theorem for a mapping $f,s$ which satisfies $s-phi$-contractive.

Keywords

• Complete cone metric spaces
• Coincidence points
• $phi$-contraction
• $s$-contraction mappings