GENERALIZATIONS OF BANACH’S CONTRACTION PRINCIPLE AND KANNAN AND CHATTERJEA’S THEOREMS FOR CYCLIC AND NONCYCLIC MAPPINGS

Two interesting extensions of Banach contraction principle to mappings that do not to be continuous, are Kannan and Chatterjea’s theorems. Before this, in the cyclical form, extensions of these two theorems and Banach contraction principle were produced. But so far, these theorems have not been studied in the noncyclical form. In this paper, we answer the question whether there are versions of these theorems for noncyclic mappings, also we give generalizations of existing results. For this purpose, in the setting of metric spaces we introduce the notions of cyclic and noncyclic contraction of Fisher type. We establish the existence of fixed points for these mappings and iterative algorithms are furnished to determine such fixed points. As a result of our results we give new theorems for cyclic orbitalcontractions.