About nonlinear contractive conditions on cone metric spaces

Abstract

In the present work we shall show that nonlinear contractive conditions on TVS-cone metric spaces can be reduced to nonlinear contractive conditions on usual metric spaces. Our results extend the results of Du (2010) [W.S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010), 2259-2261] and results of Abdeljawad and Rezapour [T. Abdeljawad, Sh. Rezapour, Some fixed point results in TVS-cone metric spaces, Fixed Point Theory (to appear 2012)].