Metric conditions, graphic contractions and weakly Picard operators

Alexandru-Darius Filip

Abstract


In the paper of S. Park (\emph{Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces}, Adv. Theory Nonlinear Anal. Appl., {\bf 7}(2023), No. 2, 455-472), the author solves the following problem: \emph{Which metric conditions imposed on \(f\) imply that \(f\) is a graphic contraction?}In this paper we study the following problem: \emph{Which metric conditions imposed on \(f\) imply that \(f\) satisfies the conditions of Rus saturated principle of graphic contractions?}

Keywords


metric space; generalized metric space; contraction type mapping; metric condition; graphic contraction; successive approximation; Picard mapping; pre-weakly Picard mapping; weakly Picard mapping; interpolative Hardy-Rogers mapping

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2025.1.11

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