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Homi-repair under iteration (I): removable and jumping cases

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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.

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Authors and Affiliations

  1. School of Mathematics and Physics, Leshan Normal University, Leshan, 614000, Sichuan, China

    Xiaohua Liu

  2. Department of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Liu Liu

  3. School of Mathematics, Sichuan University, Chengdu, 611730, Sichuan, China

    Weinian Zhang

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  1. Xiaohua Liu
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  2. Liu Liu
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  3. Weinian Zhang
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Correspondence to Liu Liu.

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Supported by Scientific Research Fund of Sichuan Provincial Education Department under Grant 18ZA0242 (Xiaohua Liu) and NSFSC Grant #2022NSFSC1812 (Liu Liu) and NSFC # 12171336 and # 11831012 (Weinian Zhang).

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Liu, X., Liu, L. & Zhang, W. Homi-repair under iteration (I): removable and jumping cases. Aequat. Math. 98, 351–379 (2024). https://doi.org/10.1007/s00010-024-01035-7

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  • DOI: https://doi.org/10.1007/s00010-024-01035-7

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