Yazar "Kaplan, Huseyin" seçeneğine göre listele

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    A New Study on the Strongly Lacunary Quasi Cauchy Sequences
    (AMER INST PHYSICS, 2018) Cakalli, Huseyin; Kaplan, Huseyin
    In this paper, the concept of a strongly lacunary delta(2) quasi-Cauchy sequence is introduced. We proved interesting theorems related to strongly lacunary delta(2) -quasi-Cauchy sequences. A real valued function f defined on a subset A of the set of real numbers, is strongly lacunary delta(2) ward continuous on A if it preserves strongly lacunary delta(2) quasi-Cauchy sequences of points in A, i.e. (f(alpha(k))) is a strongly lacunary delta(2) quasi-Cauchy sequence whenever (alpha(k)) is a strongly lacunary delta(2) quasi-Cauchy sequences of points in A, where a sequence (alpha(k)) is called strongly lacunary delta(2) quasi-Cauchy if (Delta(2)alpha(k)) is a strongly lacunary delta(2) quasi-Cauchy sequence where Delta(2)alpha(k) = alpha(k+2)-2 alpha(k+1)+ alpha(k) for each positive integer k.
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    Strongly lacunary delta ward continuity
    (AMER INST PHYSICS, 2015) Cakalli, Huseyin; Kaplan, Huseyin; Ashyralyev, A; Malkowsky, E; Lukashov, A; Basar, F
    In this paper, the concepts of a lacunary statistically delta-quasi-Cauchy sequence and a strongly lacunary delta-quasiCauchy sequence are introduced, and investigated. In this investigation, we proved interesting theorems related to some newly defined continuities here, mainly, lacunary statistically delta-ward continuity, and strongly lacunary delta-ward continuity. A real valued function f defined on a subset A of R, the set of real numbers, is called lacunary statistically delta ward continuous on A if it preserves lacunary statistically delta quasi-Cauchy sequences of points in A, i.e. (f (alpha(k))) is a lacunary statistically quasi-Cauchy sequence whenever (alpha(k)) is a lacunary statistically quasi-Cauchy sequences of points in A, and a real valued function f defined on a subset A of R is called strongly lacunary delta ward continuous on A if it preserves strongly lacunary delta quasi-Cauchy sequences of points in A, i.e. (f (alpha(k))) is a strongly lacunary quasi-Cauchy sequence whenever (alpha(k)) is a strongly lacunary quasi-Cauchy sequences of points in A. It turns out that the uniform limit process preserves such continuities.
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    A Study on N-theta-Quasi-Cauchy Sequences
    (HINDAWI LTD, 2013) Cakalli, Huseyin; Kaplan, Huseyin
    Recently, the concept of N-theta-ward continuity was introduced and studied. In this paper, we prove that the uniform limit of N-theta-ward continuous functions is N-theta-ward continuous, and the set of all N-theta-ward continuous functions is a closed subset of the set of all continuous functions. We also obtain that a real function f defined on an interval E is uniformly continuous if and only if (f (alpha(k))) is N-theta-quasi-Cauchy whenever (alpha(k)) is a quasi-Cauchy sequence of points in E.
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    A VARIATION ON LACUNARY STATISTICAL QUASI CAUCHY SEQUENCES
    (ANKARA UNIV, FAC SCI, 2017) Cakalli, Huseyin; Kaplan, Huseyin
    In this paper, the concept of a lacunary statistically delta-quasi-Cauchy sequence is investigated. In this investigation, we proved interesting theorems related to lacunary statistically delta-ward continuity, and some other kinds of continuities. A real valued function f defined on a subset A of R, the set of real numbers, is called lacunary statistically S ward continuous on A if it preserves lacunary statistically delta quasi-Cauchy sequences of points in A, i.e. (f (alpha(k))) is a lacunary statistically delta quasi-Cauchy sequence whenever (alpha(k)) is a lacunary statistically delta quasi-Cauchy sequence of points in A, where a sequence (alpha(k)) is called lacunary statistically delta quasi-Cauchy if (Delta alpha(k)) is a lacunary statistically quasi-Cauchy sequence. It turns out that the set of lacunary statistically delta ward continuous functions is a closed subset of the set of continuous functions.
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    A VARIATION ON STRONGLY LACUNARY WARD CONTINUITY
    (UNIV PRISHTINES, 2016) Cakalli, Huseyin; Kaplan, Huseyin
    In this paper, the concept of a strongly lacunary delta-quasi-Cauchy sequence is investigated. A real valued function f defined on a subset A of R, the set of real numbers, is called strongly lacunary delta ward continuous on A if it preserves strongly lacunary delta quasi-Cauchy sequences of points in A, i.e. (f(alpha(k))) is a strongly lacunary delta quasi-Cauchy sequence whenever (alpha(k)) is a strongly lacunary delta quasi-Cauchy sequences of points in Lambda, where a sequence (alpha(k)) is called strongly lacunary delta quasi-Cauchy if (Delta(alpha k)) is a strongly lacunary quasi-Cauchy sequence where Delta(2 alpha)k = alpha(k+2)-2 alpha(k+1) + alpha(k) for each positive integer k. It turns out that the set of strongly lacunary delta ward continuous functions is a closed subset of the set of continuous functions.
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    Variations on strong lacunary quasi-Cauchy sequences
    (INT SCIENTIFIC RESEARCH PUBLICATIONS, 2016) Kaplan, Huseyin; Cakalli, Huseyin
    We introduce a new function space, namely the space of N-theta(alpha)(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-theta(alpha)(p)-ward continuous if it preserves N-theta(alpha)(p)-quasi-Cauchy sequences, that is, (f(x(n))) is an N-theta(alpha)(p)-quasi-Cauchy sequence whenever (x(n)) is N-theta(alpha)(p)-quasi-Cauchy sequence of points in A, where a sequence (x(k)) of points in R is called N-theta(alpha)(p)-quasi-Cauchy if lim(r ->infinity) 1/h(r)(alpha) Sigma(k is an element of lr) vertical bar Delta x(k)vertical bar(p) = 0, where Delta x(k) = x(k+1) - x(k) for each positive integer k, p is a constant positive integer, alpha is a constant in ]0,1], I-r = (k(r-1), k(r)] and theta = (k(r)) is a lacunary sequence, that is, an increasing sequence of positive integers such that k(0) not equal 0, and h(r) : k(r) - k(r-1) -> infinity. Some other function spaces are also investigated. (C) 2016 All rights reserved.
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    Variations on strongly lacunary quasi Cauchy sequences
    (AMER INST PHYSICS, 2016) Kaplan, Huseyin; Cakalli, Huseyin; Ashyralyev, A; Lukashov, A
    We introduce a new function space, namely the space of N-theta(p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. N-theta(alpha)(p)-ward continuity is also introduced and investigated for any fixed 0 < a <= 1, and for any fixed positive integer p. A real valued function f defined on a subset A of R, the set of real numbers is N-theta(alpha)(p)-ward continuous if it preserves N-theta(alpha)(p)-quasi-Cauchy sequences, i.e. (f(x(n))) is an N-theta(alpha)(p)-quasi--Cauchy sequence whenever (x(n)) is N-theta(alpha)(p)-quasi-Cauchy sequence of points in A, where a sequence (x(k)) of points in R is called N-theta(alpha)(p)-quasi-Cauchy if [GRAPHICS] 1/h(r)(alpha) [GRAPHICS] vertical bar Delta x(k)vertical bar(p) - 0, where Delta x(k) = x(k+1) - x(k) for each positive integer k, p is a fixed positive integer, alpha is fixed in ]0, 1], I-r = (k(r-1), k(r)], and theta = (k(r)) is a lacunary sequence, i.e. an increasing sequence of positive integers such that k(0) not equal 0, and h(r) : k(r) - k(r-1) -> infinity.