Fixed Points of Sequence of Ćirić Generalized Contractions of Perov Type

Abstract

© 2016, Springer International Publishing. Perov used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article, we study fixed point results for the new extensions of sequence of Ćirić generalized contractions on cone metric space, and we give some generalized versions of the fixed point theorem of Perov. The theory is illustrated with some examples. It is worth mentioning that the main result in this paper could not be derived from Ćirić’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.