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I need this reference, but I couldn't find it online as a PDF. Any help please?

J. Sun, X, Zhang, The fixed point theorem of convex-power condensing operator and applications to abstract semilinear evolution equations, Acta Math. Sinica (in Chinese) 48 (2005) 339–446.

If you have any other paper which contains the following result, please let me know.

If $H\subseteq \mathcal{C}(I,E)$ is equicontinuous and $x_0\in \mathcal{C}(I,E)$, then $\overline{\mathrm{co}}(H\cup \{x_0\})$ is also equicontinuous in $\mathcal{C}(I,E)$,

where $\overline{\mathrm{co}}$ is the closure of the hull convex, and $\mathcal{C}(I, E)$ the space of all continuous functions $u:I\rightarrow E$, where $I\subset \mathbb{R}$, and $E$ a Banach space.

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  • $\begingroup$ Isn't this obvious? An inequality $|f(s)-f(t)|\le \varepsilon$ for $f\in H\cup\{x_0\}$ passes to the convex hull and uniform closure. $\endgroup$
    – Jochen Wengenroth
    Commented Oct 5, 2020 at 11:25
  • $\begingroup$ @Jochen Wengenroth Yeah, I know that it's easy to prove this result, but i don't wnat to prove it, i just want to cite a paper which contains the result $\endgroup$
    – Motaka
    Commented Oct 5, 2020 at 11:27

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It is online and freely accessible, but the web site of the journal is somewhat crippled. This site does not work at all for me

http://actamath.com/EN/abstract/abstract1243.shtml#

but I managed to download it from

http://actamath.com/EN/volumn/volumn_1555.shtml#

(follow the pdf link and if needed rename the file with a pdf extension).

OCR instructions: the pdf file downloaded from the web site has a corrupted layer of text, so to be able to enter it in Google translate you first need to redo the OCR. For that purpose a screen shot of a page suffices, which you can then pass on to your favorite OCR application (I used Adobe Acrobat).

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  • $\begingroup$ Thank you, unfortunately the paper is written in Chinese $\endgroup$
    – Motaka
    Commented Oct 5, 2020 at 11:31
  • $\begingroup$ I don't quite understand this; you say you "just want to cite a paper which contains the result", then the language should not matter, should it? you could in any case enter the chinese text into Google translate for a rough translation. $\endgroup$
    – Carlo Beenakker
    Commented Oct 5, 2020 at 13:17
  • $\begingroup$ first sorry if there is any misunderstanding. trying to translate the text is the first thing I tried to do, but unfortunately the text doesn't copy itself properly. $\endgroup$
    – Motaka
    Commented Oct 5, 2020 at 13:46
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    $\begingroup$ yes, the text layer in the pdf is corrupted, I have added instructions on how to repair that in the answer box $\endgroup$
    – Carlo Beenakker
    Commented Oct 5, 2020 at 15:47

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