A New Variation on Statistically Quasi Cauchy Sequences
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Date
2018
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Publisher
AMER INST PHYSICS
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info:eu-repo/semantics/closedAccess
Abstract
A sequence (alpha(k)) of real numbers is called lambda-statistically upward quasi-Cauchy if for every epsilon > 0 lim(n ->infinity 1/)lambda(n)vertical bar{k is an element of I-n : alpha(k) - alpha(k+1) >= epsilon}vertical bar = 0, where (lambda(n)) is a non-decreasing sequence of positive numbers tending to so such that lambda(n+1) <= lambda(n) +1, lambda(l) = 1, and I-n = [n - lambda(n) + 1,n] for any positive integer n. A real valued function f defined on a subset of R, the set of real numbers is lambda-statistically upward continuous if it preserves lambda-statistical upward quasi-Cauchy sequences. It turns out that the set of lambda-statistical upward continuous is a proper subset of the set of uniformly continuous functions.
Description
International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 25-30, 2017 -- Thessaloniki, GREECE
Keywords
Statistical convergence, quasi-Caudiy sequences, continuity
Journal or Series
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)
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N/A
Volume
1978
