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 Ili and Rakoevi [D. Ili, V. Rakoevi, Quasi-contractions on a cone metric space, Appl. Math. Lett. 22 (2009) 728731] and Kadelburg, Radenovi and Rakoevi [Z. Kadelburg, S. Radenovi, V. Rakoevi, Remarks on quasi-contractions on a cone metric space, Appl. Math. Lett. 22 (2009) 16741679]. © 2011 Elsevier Ltd. All rights reserved.