Fixed Point Theorems in M-distance Spaces

Babenko, Vladyslav; Babenko, Vira; Kovalenko, Oleg

doi:10.48550/arxiv.2103.13914

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Cauchy Structures Defined By Distance Functions1

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2023

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“…which is consistent with the definition of convergence in almost all previously considered spaces, in particular in usual metric spaces, in partial metric spaces [18], dualistic partial metric spaces [22], dislocated metric spaces [12], metric-like spaces [3], distance spaces [16], metric and distance spaces with more general than R sets of values of a distance function (K-metric spaces, cone metric spaces, M-distance spaces, probabilistic metric spaces, fuzzy metric spaces, and others; see [4] and references therein).…”

Section: Cauchy Structures Defined By Distance Functionsmentioning

confidence: 99%

Fixed sets and fixed points for mappings in generalized $\rm Lim$-spaces of Fréchet

Бабенко

Коваленко

2023

Carpathian Math. Publ.

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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.

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