Yazar "Sengul, Hacer" seçeneğine göre listele

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    A variation on lacunary quasi Cauchy sequences
    (Amer Inst Physics, 2016) Cakalli, Huseyin; Et, Mikail; Sengul, Hacer
    In the present paper, we introduce a concept of ideal lacunary statistical quasi-Cauchy sequence of order alpha of real numbers in the sense that a sequence (x(k)) of points in R is called I lacunary statistically quasi-Cauchy of order alpha, if {r is an element of N : 1/h(r)(a) vertical bar Delta x(k)vertical bar >= epsilon vertical bar >= epsilon vertical bar >= delta}is an element of I for each epsilon > 0 and for each delta > 0, where an ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. The main purpose of this paper is to investigate ideal lacunary statistical ward continuity of order alpha, where a function f is called I lacunary statistically ward continuous of order alpha if it preserves I-lacunary statistically quasi-Cauchy sequences of order alpha, i.e. (f(x(n))) is a s(theta)(alpha)(I)-quasi-Cauchy sequence whenever (x(n)) is.
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    f- Lacunary Statistical Convergence Of Order (?,?)
    (Amer Inst Physics, 2017) Sengul, Hacer; Isik, Mahmut; Et, Mikail
    The main purpose of this paper is to introduce the concepts of f-lacunary statistical convergence of order (alpha,beta) and strong f-lacunary summability of order (alpha,beta) of sequences of real numbers for 0 < alpha <= beta <= 1, where f is an unbounded modulus.
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    On (?, I)-Statistical Convergence of Order ? of Sequences of Function
    (Natl Acad Sciences India, 2018) Sengul, Hacer; Et, Mikail
    In this paper, we introduce the concepts of pointwise (lambda, I)-statistical convergence of order alpha and pointwise w(p)(lambda, I)-summability of order alpha. Also some relations between pointwise (lambda, I)-statistical convergence of order alpha and pointwise w(p)(lambda, I)-summability of order alpha are given.
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    ON (?m, I) - LACUNARY STATISTICAL CONVERGENCE OF ORDER ?
    (Univ Prishtines, 2016) Et, Mikail; Sengul, Hacer
    In this study, using the generalized difference operator Delta(m), we introduce the concepts of (Delta(m) , I) -lacunary statistical convergence of order alpha and lacunary strong Delta(m)(p)-summability of order alpha of sequences and give some relations about these concepts.
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    On asymptotically lacunary statistical equivalent of order a of difference sequences
    (Amer Inst Physics, 2015) Et, Mikail; Sengul, Hacer; Cinar, Muhammed
    In this study, we introduce and examine the concepts of 4-asymptotically statistical equivalent of order a and strong Delta(m)(theta) asymptotically equivalent of order a of sequences. Also, we give some relations connected to these concepts.
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    On I - Lacunary Statistical Convergence of Order ? of Sequences of Sets
    (Univ Nis, Fac Sci Math, 2017) Sengul, Hacer; Et, Mikail
    The idea of I-convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P.;. Salat, T. and Wilczynski, W. I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle, W. H. Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245(2) (2000), 513-527]. In this paper we introduce the concepts of Wijsman I-lacunary statistical convergence of order alpha and Wijsman strongly I-lacunary statistical convergence of order alpha, and investigated between their relationship.
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    ON LACUNARY STATISTICAL BOUNDEDNESS OF ORDER ?
    (Univ Nis, 2016) Et, Mikail; Mohiuddine, Syed A.; Sengul, Hacer
    The aim of this paper is to introduce and examine the concept of lacunary statistical boundedness of order alpha and give the relations between statistical boundedness and lacunary statistical boundedness of order alpha.
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    On Pointwise Lacunary Statistical Convergence of Order ? of Sequences of Function
    (Natl Acad Sciences India, 2015) Et, Mikail; Sengul, Hacer
    In this paper we introduce the concepts of pointwise lacunary statistical convergence of order alpha and pointwise w(p)(f, theta)-summability of order alpha of sequences of real valued functions. Also some relations between pointwise S-theta(f)(f)-statistical convergence and pointwise w(p)(alpha)(f, theta)-summability are given.
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    SOME CESARO-TYPE SUMMABILITY SPACES DEFINED BY A MODULUS FUNCTION OF ORDER (?, ?)
    (Ankara Univ, Fac Sci, 2017) Sengul, Hacer
    In this article, we introduce strong w [theta, f, p]-summability of order (alpha, beta) for sequences of complex (or real) numbers and give some inclusion relations between the sets of lacunary statistical convergence of order (alpha,beta), strong omega(beta)(alpha) [theta, f, p] summability and strong omega(beta)(alpha)(p)-summability.
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    Some Cesaro-Type Summability Spaces of Order ? and Lacunary Statistical Convergence of Order ?
    (Univ Nis, Fac Sci Math, 2014) Et, Mikail; Sengul, Hacer
    In the paper [32], we have defined the concepts of lacunary statistical convergence of order ff and strong N-theta(p)-summability of order ff for sequences of complex (or real) numbers. In this paper we continue to examine others relations between lacunary statistical convergence of order alpha and strong N-theta(p)-summability of order alpha.
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    Some Geometric Properties of Generalized Difference Cesaro Sequence Spaces
    (Chiang Mai Univ, Fac Science, 2017) Sengul, Hacer; Et, Mikail
    In this paper, we define the generalized Cesaro difference sequence space C-(p) (Delta(m)) and consider it equipped with the Luxemburg norm under which it is a Banach space and we show that in the space C-(p) (Delta(m)) every weakly convergent sequence on the unit sphere converges is the norm, where p - (p(n)) is a bounded sequence of positive real numbers with p(n) > 1 for all n is an element of N.