Yazar "Ersan, Sibel" seçeneğine göre listele

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    Lacunary Ward Continuity in 2-normed Spaces
    (UNIV NIS, FAC SCI MATH, 2015) Cakalli, Huseyin; Ersan, Sibel
    In this paper, we introduce lacunary statistical ward continuity in a 2-normed space. A function f defined on a subset E of a 2-normed space X is lacunary statistically ward continuous if it preserves lacunary statistically quasi-Cauchy sequences of points in E where a sequence (x(k)) of points in X is lacunary statistically quasi-Cauchy if lim(r ->infinity) 1/h(r) vertical bar{k is an element of I-r : parallel to x(k+1) - x(k), z parallel to >= epsilon}vertical bar = 0 for every positive real number epsilon and z 1/4 X, and (k(r)) is an increasing sequence of positive integers such that k(0) = 0 and h(r) = k(r) - k(r-1) -> infinity as r -> infinity, I-r = (k(r-1), k(r)]. We investigate not only lacunary statistical ward continuity, but also some other kinds of continuities in 2-normed spaces.
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    New Types of Continuity in 2-Normed Spaces
    (UNIV NIS, FAC SCI MATH, 2016) Cakalli, Huseyin; Ersan, Sibel
    A sequence (chi(n)) of points in a 2-normed space X is statistically quasi-Cauchy if the sequence of difference between successive terms statistically converges to 0. In this paper we mainly study statistical ward continuity, where a function defined on a subset E of X is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in E. Some other types of continuity are also discussed, and interesting results related to these kinds of continuity are obtained in 2-normed space setting.
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    On ?-statistical convergence in neutrosophic normed spaces
    (Walter De Gruyter Gmbh, 2023) Ersan, Sibel
    In this study, the concept of rho-statistical convergence with respect to the neutrosophic norm in the neutrosophic normed spaces is introduced. Some properties and some inclusion theorems related to this concept are investigated.
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    p-ward continuity in 2-normed spaces
    (Maltepe Üniversitesi, 2019) Ersan, Sibel
    In this paper, the concept of a quasi-Cauchy sequence is generalized to a concept of a p-quasi-Cauchy sequence for any fixed positive integer p in 2-normed space X. Some interesting theorems related to p-ward continuity and uniform continuity are obtained. A sequence (xn) in a 2-normed space X is called p-quasiCauchy if limn??
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    Strongly Lacunary delta-quasi-Cauchy sequences in 2-normed spaces
    (AMER INST PHYSICS, 2019) Ersan, Sibel; Cakalli, H; Kocinac, LDR; Harte, R; Cao, J; Savas, E; Ersan, S; Yildiz, S
    A sequence (x(k)) of points in a subset E of a 2-normed space X is called strongly lacunary delta-quasi-Cauchy, or N-theta-delta-quasi-Cauchy if (Delta x(k)) is N-theta-convergent to 0, that is lim(r ->infinity) 1/h(r) Sigma(k is an element of Ir) parallel to Delta(2)x(k), Z parallel to = 0 for every fixed z is an element of X. A function defined II on a subset E of X is called strongly lacunary delta-ward continuous if it preserves N-theta-delta-quasi-Cauchy sequences, i.e. (f(x(k))) is an N-theta-delta-quasi-Cauchy sequence whenever (x(k)) is. In this study we obtain some theorems related to strongly lacunary delta-quasi-Cauchy sequences.
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    Strongly Lacunary Ward Continuity in 2-Normed Spaces
    (HINDAWI LTD, 2014) Cakalli, Huseyin; Ersan, Sibel
    A function.. defined on a subset.. of a 2-normed space.. is strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points in E; that is, (f(x(k))) is a strongly lacunary quasi-Cauchy sequence whenever (x(k)) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.
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    Variation on Strongly Lacunary delta Ward Continuity in 2-normed Spaces
    (Soc Paranaense Matematica, 2020) Ersan, Sibel
    A sequence (x(k)) of points in a subset E of a 2-normed space X is called strongly lacunary delta-quasi-Cauchy, or N-theta-delta-quasi-Cauchy if (Delta x(k)) is N-theta-convergent to 0, that is lim(r ->infinity) 1/h(r) Sigma(k is an element of Ir) parallel to Delta(2) x(k), z parallel to = 0 for every fixed z is an element of X. A function defined on a subset E of X is called strongly lacunary delta-ward continuous if it preserves N-theta-delta-quasi-Cauchy sequences, i.e. (f(x(k))) is an N-theta-delta-quasi-Cauchy sequence whenever (x(k)) is. In this study we obtain some theorems related to strongly lacunary delta-quasi-Cauchy sequences.
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    Ward Continuity in 2-Normed Spaces
    (UNIV NIS, FAC SCI MATH, 2015) Ersan, Sibel; Cakalli, Huseyin
    In this paper, we introduce and investigate the concept of ward continuity in 2-normed spaces. A function f defined on a 2-normed space (X, parallel to., .parallel to) is ward continuous if it preserves quasi-Cauchy sequences, where a sequence (x(n)) of points in X is called quasi-Cauchy if lim(n ->infinity) parallel to Lambda x(n,) z parallel to = 0 for every z is an element of X. Some other kinds of continuities are also introduced, and interesting theorems are proved in 2-normed spaces.