New Type Continuities via Abel Convergence
نویسندگان
چکیده
منابع مشابه
New Type Continuities via Abel Convergence
We investigate the concept of Abel continuity. A function f defined on a subset of ℝ, the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a sequence of Abel continuous functions is Abel continuous and the set of Abel continuous functions is...
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and Applied Analysis 3 Proof. The proof follows from Theorem 2.1. The following theorem shows that on a slowly oscillating compact subset A of R, slowly oscillating continuity implies uniform continuity. Theorem 2.3. Let A be a slowly oscillating compact subset of R and let f : A → R be slowly oscillating continuous on A. Then f is uniformly continuous on A. Proof. Assume that f is not uniforml...
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ژورنال
عنوان ژورنال: The Scientific World Journal
سال: 2014
ISSN: 2356-6140,1537-744X
DOI: 10.1155/2014/398379