Akram Safari-Hafshejani - Department of Pure Mathematics, Payame Noor University, P. O. Box: ۱۹۳۹۵-۳۶۹۷, Tehran, Iran

‎Two interesting extensions of Banach contraction principle to mappings that don't 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 non-cyclic 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 orbital contractions‎.

Fixed point‎, ‎Cyclic and non-cyclic contractions of Fisher-type‎, ‎Kannan and Chatterjea mappings‎, ‎cyclic orbital contraction