Peer-Reviewed Article May 5, 2014
Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality
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Published in: Fixed Point Theory and Applications
Publisher: Springer Nature • Egypt • 1687-1812
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). MSC: 54H25, 47H10.