Remarks on asymptotic regularity and fixed points

By J. Górnicki. Journal of Fixed Point Theory and Applications, 2019

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Asymptotic regularity allows to provide simple proofs of Banach’s theorem and Kannan’s theorem. Using asymptotic regularity and Kannan’s type conditions we generalize these results, in particular, the Banach contraction principle (see Theorem 2.6 and Corollary 2.10). Further, we discuss the analogous results for monotone mappings on preordered metric spaces, where a preordered binary relation is weaker than a partial order. Next, we will prove a random version of the presented deterministic fixed-point theorems.

Subfields: Astronomy and Astrophysics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/97f6d06f719e29c2c46487f307b485832a4c33d3