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Variations on strong lacunary quasi-Cauchy sequences

2016
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Journal of Nonlinear Science and its Applications
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We introduce a new function space, namely the space of N α 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 N α θ (p)-ward continuous if it preserves N α θ (p)-quasi-Cauchy sequences, that is, (f (x n )) is an N α θ (p)-quasi-Cauchy sequence whenever (x n ) is N α θ (p)-quasi-Cauchy sequence of points in A, where a sequence (x k ) of points in R is

doi:10.22436/jnsa.009.06.77
fatcat:mjo57j2vg5cdvaxgx3zszgadri