Çakallı, Hüseyin2024-07-122024-07-122008Çakallı, H. (2008). Slowly oscillating continuity. Abstract and Applied Analysis. Hindawi. s. 1-5.10.1155/2008/4857062-s2.0-43949092733https://www.hindawi.com/journals/aaa/2008/485706/https://doi.prg/10.1155/2008/485706https://hdl.handle.net/20.500.12415/2028A function is continuous if and only if, for each point in the domain, , whenever . This is equivalent to the statement that is a convergent sequence whenever is convergent. The concept of slowly oscillating continuity is defined in the sense that a function is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, is slowly oscillating whenever is slowly oscillating. A sequence of points in is slowly oscillating if , where denotes the integer part of . Using 's and 's, this is equivalent to the case when, for any given , there exist and such that if and . A new type compactness is also defined and some new results related to compactness are obtained.eninfo:eu-repo/semantics/openAccessArticle51WOS:000255607900001Q2