{"title":"Homi-repair under iteration (I): removable and jumping cases","authors":"Xiaohua Liu, Liu Liu, Weinian Zhang","doi":"10.1007/s00010-024-01035-7","DOIUrl":null,"url":null,"abstract":"<div><p>It was found that a function with exactly one discontinuity may have a continuous iterate of second order, indicating that a discontinuity may be repaired to be a continuous one by its adjacent pair of functions of second order, called second order <img> sui-repair. If a function has more than one discontinuities, examples show that some discontinuities may be repaired to be continuous ones by the other’s adjacent pair of functions of second order, called second order <span>\\(C^{0}\\)</span> homi-repair. In this paper we investigate second order <span>\\(C^{0}\\)</span> homi-repairs of removable and jumping discontinuities for functions having more than one but finitely many discontinuities. We give necessary and sufficient conditions for removable and jumping discontinuities to be <span>\\(C^0\\)</span> repaired by the second order iteration.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 2","pages":"351 - 379"},"PeriodicalIF":0.9000,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01035-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
It was found that a function with exactly one discontinuity may have a continuous iterate of second order, indicating that a discontinuity may be repaired to be a continuous one by its adjacent pair of functions of second order, called second order sui-repair. If a function has more than one discontinuities, examples show that some discontinuities may be repaired to be continuous ones by the other’s adjacent pair of functions of second order, called second order \(C^{0}\) homi-repair. In this paper we investigate second order \(C^{0}\) homi-repairs of removable and jumping discontinuities for functions having more than one but finitely many discontinuities. We give necessary and sufficient conditions for removable and jumping discontinuities to be \(C^0\) repaired by the second order iteration.
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
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