On (α,p)-Cyclic Contractions and Related Fixed Point Theorems

Lipschitz mapping appears inevitably in many branches of mathematics, especially in functional analysis, and leads to the study of new results in metric fixed point theory. Goebel and Sims (resp. Goebel and Japon-Pineda) introduced a class of the Lipschitz mappings termed as (α,p)-Liptschitz mapping...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-10, Vol.15 (10), p.1826
Main Authors: Asem, Victory, Singh, Yumnam Mahendra, Khan, Mohammad Saeed, Sessa, Salvatore
Format: Article
Language:English
Subjects:
(α,p)-Chatterjea-type contraction
(α,p)-cyclic contraction
(α,p)-Kannan-type contraction
Codes
fixed point
Fixed points (mathematics)
Fredholm equations
Functional analysis
Inequality
Integral equations
Lipschitz condition
Metric space
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Summary:Lipschitz mapping appears inevitably in many branches of mathematics, especially in functional analysis, and leads to the study of new results in metric fixed point theory. Goebel and Sims (resp. Goebel and Japon-Pineda) introduced a class of the Lipschitz mappings termed as (α,p)-Liptschitz mappings and studied not only the modified form of the Lipschitz condition, but also the behavior of a finite number of their iterates. The purpose of this paper is to discuss the various types of (α,p)-contractions with cyclic representation that extend the results due to Banach, Kannan, and Chatterjea. Moreover, based on such types of contractions and the property of symmetry, we obtain some related fixed-point results in the setting of metric spaces. Some examples are studied to illustrate the validity of our obtained results. As an application of our results, we establish the existence of the solution to a class of Fredholm integral equations.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15101826