Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality

Abstract

In this paper, we first present some elementary results concerning cone metric spaces over Banach algebras. Next, by using these results and the related ones about c-sequence on cone metric spaces we obtain some new fixed point theorems for the generalized Lipschitz mappings on cone metric spaces over Banach algebras without the assumption of normality. As a consequence, our main results improve and generalize the corresponding results in the recent paper by Liu and Xu (Fixed Point Theory Appl. 2013:320, 2013). © 2014 Xu and Radenović; licensee Springer.