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

  • V.F. Babenko Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine
  • V.V. Babenko Drake University, 2507 University avenue, Des Moines, USA
  • O.V. Kovalenko Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine
Keywords: fixed point theorem, family of Cauchy sequences, Fréchet limit space
Published online: 2023-06-30

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.

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How to Cite
(1)
Babenko V., Babenko V., Kovalenko O. Fixed Sets and Fixed Points for Mappings in Generalized $\rm Lim$-Spaces of Fréchet. Carpathian Math. Publ. 2023, 15 (1), 260-269.