Generalizations of Banach's contraction principle and Kannan and Chatterjea's theorems for cyclic and non-cyclic mappings

Document Type : Research Paper

Author

Department of Pure Mathematics, Payame Noor University, P. O. Box: 19395-3697, Tehran, Iran

Abstract

‎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.

Keywords

References

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History

  • Receive Date: 12 July 2022
  • Revise Date: 12 August 2022
  • Accept Date: 18 January 2023

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