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۱Variations on strong lacunary quasi–Cauchy sequences
نویسنده(ها): ،
اطلاعات انتشار: Journal of Nonlinear Sciences and Applications، نهم،شماره۶، ۲۰۱۶، سال
تعداد صفحات: ۳۰۱۰
We introduce a new function space, namely the space of Nα θ (p)–ward continuous functions, which turns out to be a closed subspace of the space of continuous functions. A real valued function f defined on a subset A of R, the set of real numbers, is Nα θ (p)–ward continuous if it preserves Nα θ (p)–quasi–Cauchy sequences, that is, (f(xn)) is an Nα θ (p)–quasi–Cauchy sequence whenever (xn) is Nα θ (p)–quasi–Cauchy sequence of points in A, where a sequence (xk) of points in R is called Nα θ (p)–quasi–Cauchy ifwhere ∆xk = xk+1 −xk for each positive integer k, p is a constant positive integer, α is a constant in ]0,1], Ir = (kr−1,kr], and θ = (kr) is a lacunary sequence, that is, an increasing sequence of positive integers such that k0 6= 0, and hr : kr −kr−1 →∞. Some other function spaces are also investigated.
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