On nonlinear quasi-contractions on TVS-cone metric spaces

Abstract

Recently, Du [W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. (2009), doi:10.1016/j.na.2009.10.026] introduced the notion of TVS-cone metric space. In this paper we present fixed point theorem for nonlinear quasi-contractive mappings defined on TVS-cone metric space, which generalizes earlier results obtained by Ilic and Rakocevic [D. Ilic, V. Rakocevic, Quasi-contractions on a cone metric space, Appl. Math. Lett. 22 (2009) 728-731] and Kadelburg, Radenovic and Rakocevic [Z. Kadelburg, S. Radenovic, V. Rakocevic, Remarks on quasi-contractions on a cone metric space, Appl. Math. Lett. 22 (2009) 1674-1679].