Convergence results for controlled contractions and applications to a system of Volterra integral equations

This work presents the concept of controlled dislocated metric spaces, and the Banach contraction principle in these spaces is examined. Next, we provide extensive examples of numerical convergence of fixed points to demonstrate the practical implications of such spaces. Along with specific instance...

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Bibliographic Details
Published in:Applied mathematics in science and engineering 2024-12, Vol.32 (1)
Main Authors: Guo, Lifang, Younis, Mudasir, Ahmad, Haroon, Özturk, Mahpeyker, Din, Fahim Ud, Ahmad, Shahbaz
Format: Article
Language:English
Subjects:
47H10
47J25
Common fixed point
dislocated controlled metric type space
rational contraction
Volterra integral equation
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Summary:This work presents the concept of controlled dislocated metric spaces, and the Banach contraction principle in these spaces is examined. Next, we provide extensive examples of numerical convergence of fixed points to demonstrate the practical implications of such spaces. Along with specific instances, it presents the idea of a rational contraction of the [Formula: see text]type to determine common fixed points in such spaces. Moreover, numerical analysis and graphical comparisons are used to further assess the existence of common fixed points based on the provided notions. Lastly, using these ideas to solve a Volterra integral equation shows how useful they are for finding common solutions, improving our comprehension of fixed point theory in these spaces, and creating new avenues for applications.
ISSN:2769-0911
2769-0911
DOI:10.1080/27690911.2024.2424909