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

Authors

  • 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
https://doi.org/10.15330/cmp.15.1.260-269

Keywords:

fixed point theorem, family of Cauchy sequences, Fréchet limit space
Published online: 2023-06-30

Abstract

In the article, we axiomatically define generalized Lim-spaces (X,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 X2, 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.

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