Slowly Oscillating Continuity

By Hüseyin Çakalli. 2008

91 citations recorded by the source corpus.

A function 𝑓 is continuous if and only if, for each point 𝑥0 in the domain, lim𝑛→∞𝑓(𝑥𝑛)=𝑓(𝑥0), whenever lim𝑛→∞𝑥𝑛=𝑥0. This is equivalent to the statement that (𝑓(𝑥𝑛)) is a convergent sequence whenever (𝑥𝑛) is convergent. The concept of slowly oscillating continuity is defined in the sense that a function 𝑓 is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, (𝑓(𝑥𝑛)) is slowly oscillating whenever (𝑥𝑛) is slowly oscillating. A sequence (𝑥𝑛) of points in 𝐑 is slowly oscillating if lim𝜆→1

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4a3301942013fd7d438b17ead248c415b1e5620b

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Citations in the corpus

• CREATING SLOWLY OSCILLATING SEQUENCES AND SLOWLY OSCILLATING CONTINUOUS FUNCTIONS (2011, background): “In [3], the author asserts that every slowly oscillating continuous function is, in fact, continuous in the ordinary sense.”