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arXiv · 2206.01155

Fixed sets and fixed points in $\Lim$--spaces]{Fixed sets and fixed points for mappings in generalized $\Lim$--spaces of Fr\'echet

Vladyslav Babenko·Vira Babenko·Oleg Kovalenko
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Abstract

In this article we discuss a possibility to implement a well-known scheme of proof for contraction mapping theorems in a situation, when convergence, families of Cauchy sequences, and contractiveness of mappings are defined axiomatically. We also consider ways to specify families of Cauchy sequences and contractiveness conditions using distance-like functions with values in some partially ordered set and establish fixed set and point theorems for generalized contractions of the \'Ciri\'c and Caristi types.

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Vladyslav Babenko, Vira Babenko, Oleg Kovalenko. 2022-06-02. Fixed sets and fixed points in $\Lim$--spaces]{Fixed sets and fixed points for mappings in generalized $\Lim$--spaces of Fr\'echet. https://doi.org/10.15330/cmp.15.1.260-269

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