7190f42e333d894d22e1e0a871576b95 mathematics_10_02415_v2.pdf 9d519270b40d2c573f4f9908225ee00beb1ea1a7 mathematics_10_02415_v2.pdf 0705453b9030040566343e30fba6556476fabf1c1a55a2a9d967e72d198650e7 mathematics_10_02415_v2.pdf Title: On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples Subject: In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets p( 2 ) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed. Keywords: cyclic self-mappings; cyclic contractions; mixed cyclic/acyclic self-mappings; uniformly convex Banach space; impulsive dynamic systems; stabilization Author: Manuel De la Sen and Asier Ibeas Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Thu Jul 14 07:41:41 2022 CEST ModDate: Thu Jul 14 09:35:44 2022 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 29 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 2573216 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- MIKRSI+VnURWPalladioL Type 1 Custom yes yes no 10 0 OVKOJQ+URWPalladioL-Bold Type 1 Custom yes yes no 15 0 DAHFSY+URWPalladioL-Roma Type 1 Custom yes yes no 20 0 LXKOKC+URWPalladioL-Ital Type 1 Custom yes yes no 24 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 28 0 KIXBBQ+CMSY10 Type 1 Builtin yes yes no 32 0 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no no 494 0 TimesNewRomanPS-ItalicMT TrueType WinAnsi no no no 497 0 Helvetica TrueType WinAnsi no no no 505 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 513 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 517 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 521 0 BCDHEE+PalatinoLinotype-Roman CID TrueType Identity-H yes yes yes 525 0 SymbolMT CID TrueType Identity-H yes no yes 532 0 TimesNewRomanPSMT TrueType WinAnsi no no no 539 0 TimesNewRomanPS-ItalicMT TrueType WinAnsi no no no 542 0 Helvetica TrueType WinAnsi no no no 550 0 CRUZTT+VnURWPalladioL-Italic Type 1 Custom yes yes no 560 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-03-03 02:37:50 CET RepresentationInformation: mathematics_10_02415_v2.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-02-25 01:34:23 CET Size: 2573216 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 671 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: Problem Statement for Two Subsets of Metric Space Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Item: Title: Problem Statement for p Subsets of a Metric Space Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Some Particular Results: The Case of Non-Expansivity and That of Monitored Switching Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Numerical Simulations Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Info: Title: On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples Author: Manuel De la Sen and Asier Ibeas Subject: In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets p( 2 ) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed. 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