A note on Arzela–Ascoli's lemma in almost periodic problems
Qiyuan Zhou
College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, 415000 Hunan, China
Search for more papers by this authorCorresponding Author
Jianying Shao
College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, 314001 Zhejiang, China
Correspondence to: Jianying Shao, College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China,
E-mail: [email protected]
Search for more papers by this authorQiyuan Zhou
College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, 415000 Hunan, China
Search for more papers by this authorCorresponding Author
Jianying Shao
College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, 314001 Zhejiang, China
Correspondence to: Jianying Shao, College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China,
E-mail: [email protected]
Search for more papers by this authorAbstract
This paper is concerned with a generalized Arzela–Ascoli's lemma, which has been extensively applied in almost periodic problems by the continuation theorem of degree theory. We give a counter example to show that this lemma is incorrect, and there is a gap in the proof of some existing literature, where the addressed generalized Arzela–Ascoli's lemma was used. Moreover, we make some final comments and introduce an open problem. Copyright © 2016 John Wiley & Sons, Ltd.
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