The (C, α) integrability of functions by weighted mean methods
Makaleler > Tam Makale · 2012
Yazarlar: İbrahim ÇANAK, Ümit Totur
Filomat, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Scopus, 2012, cilt 26, ss 1209-1214
DOI: 10.2298/FIL1206209C
Özet
Let p(x) be a nondecreasing continuous function on [0,∞) such that p(0) = 0 and p(t) → ∞ as t → ∞. For a continuous function f(x) on [0,∞), we define We say that a continuous function f(x) on [0,∞) is (C, α) integrable to a by the weighted mean method determined by the function p(x) for some α > -1 if the limit limt→∞σα(t) = a exists. We prove that if the limit limt→∞σα(t) = a exists for some α > -1, then the limit limt→∞ σα+h(t) = a exists for all h > 0. Next, we prove that if the limit limt→∞σα(t) = a exists for some α > 0 and then the limit limt→∞σα-1(t) = a exists.