Generalizations of Banach's contraction principle and Kannan and Chatterjea's theorems for cyclic and non-cyclic mappings
نوع فايل (MIME):PDF
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.
کلید واژگانFixed point
Cyclic and non-cyclic contractions of Fisher-type
Kannan and Chatterjea mappings
cyclic orbital contraction
سازمان پدید آورندهDepartment of Pure Mathematics, Payame Noor University, P. O. Box: 19395-3697, Tehran, Iran
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