Fixed sets and fixed points for mappings in generalized $\rm Lim$-spaces of Fréchet
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Published:2023-06-30
Issue:1
Volume:15
Page:260-269
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ISSN:2313-0210
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Container-title:Carpathian Mathematical Publications
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language:
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Short-container-title:Carpathian Math. Publ.
Author:
Babenko V.F.,Babenko V.V.,Kovalenko O.V.
Abstract
In the article, we axiomatically define generalized $\rm Lim$-spaces $(X,{\rm Lim})$, Cauchy structures, contractive mappings and prove an abstract version of the contraction mapping principle. We also consider ways to specify families of Cauchy sequences and contraction conditions using a base in $X^2$, distance-like or sum-like functions with values in some partially ordered set $Y$. We establish fixed set and fixed point theorems for generalized contractions of the Meir-Keeler and Taylor, Ćirić and Caristi types. The obtained results generalize many known fixed point theorems and are new even in many classical situations.
Publisher
Vasyl Stefanyk Precarpathian National University
Subject
General Mathematics