Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2008 (2008), Article ID 485706, 5 pages.
Slowly Oscillating Continuity
A 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.
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 485706, 5 pages.
First available in Project Euclid: 9 September 2008
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Çakalli, H. Slowly Oscillating Continuity. Abstr. Appl. Anal. 2008 (2008), Article ID 485706, 5 pages. doi:10.1155/2008/485706. https://projecteuclid.org/euclid.aaa/1220969159