The relation between F-contraction and Meir–Keeler contraction

Meir–Keeler contraction gives different type of insight on the idea of contractive mappings. Almost half of a century later, the notation of F -contraction appeared and it was in the center of research in the Fixed Point Theory during the last decade. Those two concepts appear totally distinct and w...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023, Vol.117 (1), Article 39
Main Author: Cvetković, Marija
Format: Article
Language:English
Subjects:
Applications of Mathematics
Fixed points (mathematics)
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
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Summary:Meir–Keeler contraction gives different type of insight on the idea of contractive mappings. Almost half of a century later, the notation of F -contraction appeared and it was in the center of research in the Fixed Point Theory during the last decade. Those two concepts appear totally distinct and without any obvious bond, except the fact that Banach contraction is both F -contraction and Meir–Keeler contraction. In this article, we discuss on its relation and give appropriate examples. It will be shown that F -contraction is a Meir–Keeler contraction, but we will also give an example that converse do not hold.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-022-01373-8