Yazar "Et, Mikail" seçeneğine göre listele

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    Deferred statistical convergence and strongly deferred summable functions
    (Maltepe Üniversitesi, 2019) Et, Mikail; Baliarsingh, P.; Şengül, Hacer
    The main purpose of this paper is to introduce and investigate the concepts of deferred strong summability and deferred statistical convergence of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,?). Some relations between deferred strong summability and deferred statistical convergence of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1, ?) are also given.
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    ??–deferred statistical convergence of fractional order
    (Maltepe Üniversitesi, 2021) Aral, Nazlım Deniz; Şengül Kandemir, Hacer; Et, Mikail
    t. In this paper, we introduce the concepts of ??-deferred statistical convergence with the fractional order of ? and ??? strongly convergence with the fractional order of ?. Additionally, we give some relations about these concepts.
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    Deferred statistical convergence of order ? in topological groups
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Et, Mikail; Çakallı, Hüseyin
    In this paper, the concept of deferred statistical convergence of order ? is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order ? in topological groups and the set of all deferred statistically convergent sequences of order ? in topological groups are given.
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    Lacunary A-statistical convergence and lacunary strong A-convergence sequences of order (?,?) with respect to a modulus
    (Amer Inst Physics, 2019) Şengül, Hacer; Et, Mikail; Cakalli, Hüseyin
    In this paper, the definitions of lacunary strong A-convergence of order (alpha,beta) with respect to a modulus and lacunary A-statistical convergence of order (alpha,beta) are given. We study some connections between lacunary strong A-convergence of order (alpha,beta) with respect to a modulus and lacunary A-statistical convergence of order (alpha,beta).
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    Lacunary a? statistical convergence and lacunary strong a? convergence of order (?, ?) with respect to a modulus
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Et, Mikail; Çakallı, Hüseyin
    In this paper, the definitions of lacunary strong A?convergence of order (?, ?) with respect to a modulus and lacunary A?statistical convergence of order (?, ?) are given. We study some connections between lacunary strong A?convergence of order (?, ?) with respect to a modulus and lacunary A?statistical convergence of order (?, ?). Interesting results are obtained.
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    Lacunary d-statistical convergence and lacunary d-statistical boundedness in metric spaces
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Et, Mikail
    In this study, using a lacunary sequence we introduce the concepts of lacunary d?statistically convergent sequences and lacunary d?statistically bounded sequences in general metric spaces.
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    Lacunary statistical convergence of difference sequences of fractional order
    (Maltepe Üniversitesi, 2019) Aral, Nazım Deniz; Et, Mikail
    The idea of statistical convergence was given by Zygmund [1] in the first edition of his monograph published in Warsaw in 1935. Over the years and under different names statistical convergence was discussed in the theory of Fourier analysis, Ergodic theory, Number theory, Measure theory, Trigonometric series, Turnpike theory and Banach spaces. In this study we introduce the concepts of ??- lacunary statistical convergence with the fractional order of ?, ? ? R and ??- lacunary strongly convergence with the fractional order of ?, ? ? R, and examine some properties of these sequence spaces. We also establish some connections between ??- lacunary strongly convergence of fractional order of ? and ?? -lacunary statistical convergence of fractional order of ?
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    ?m – weighted statistical convergence
    (Maltepe Üniversitesi, 2021) Et, Mikail; Şengül Kandemir, Hacer
    In this study, we introduce and examine the concepts of ?m?weighted statistical convergence and ?m?weighted N, pn ?summability. Also some relations between ?m?weighted statistical convergence and ?m?weighted N, pn ?summability are given.
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    N ? ?(?, I)? ward continuity
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Çakallı, Hüseyin; Et, Mikail
    The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (?, ?) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (?, ?) is also investigated. Interesting results are obtained.
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    N-alpha(beta)(theta, I)- Ward Continuity
    (AMER INST PHYSICS, 2019) Sengul, Hacer; Cakalli, Huseyin; Et, Mikail; Cakalli, H; Kocinac, LDR; Harte, R; Cao, J; Savas, E; Ersan, S; Yildiz, S
    The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (alpha, beta) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (alpha, beta) is also investigated. Interesting results are obtained.
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    On (f, I)-Lacunary Statistical Convergence of Order alpha of Sequences of Sets
    (SOC PARANAENSE MATEMATICA, 2020) Sengul, Hacer; Et, Mikail; Cakalli, Huseyin
    In this paper we introduce the concepts of Wijsman (f, I)-lacunary statistical convergence of order alpha and Wijsman strongly (f, I)-lacunary statistical convergence of order alpha, and investigated between their relationship.
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    On ?? statistical convergence
    (Maltepe Üniversitesi, 2021) Aral, Nazlım Deniz; Şengül Kandemir, Hacer; Et, Mikail
    In this study, by using definition of ?-statistical convergence which was defined by C¸ akallı[2], we give some inclusion relations between the set of ?-statistical convergence and strong (S, [?]) summability.
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    On I?deferred statistical convergence
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Et, Mikail; Işık, Mahmut
    The idea of I?convergence of real sequences was introduced by Kostyrko et al. [ Kostyrko, P., Sal´at, T. and Wilczy ´nski, ? 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 I?deferred statistical convergence and strong I?deferred Cesaro convergence and investigate between ` their relationship.
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    On lacunary d-statistical convergence of order ?
    (Maltepe Üniversitesi, 2019) Et, Mikail; Karataş, Muharrem
    The idea of statistical convergence was given by Zygmund [1] in the first edition of his monograph puplished in Warsaw in 1935. The consept of statistical convergence was introduced by Steinhaus [2] and Fast [3] and later reintroduced by Schoenberg [4]. Over the years and under different names statistical convergence was discussed in the theory of Fourier analysis, Ergodic theory, Number theory, Measure theory, Trigonometric series, Turnpike theory and Banach spaces. Later on it was further investigated from the sequence space point of view and linked with summability theory by Bhardwaj et al. [5], Bilalov and Nazarova [6], C¸ akallı et al. ([7], [8],[9]), Caserta et al. [10], C¸ ınar et al. ([11],[12]), Connor [13], Et et al. ([14],[15]), Fridy [16], Fridy and Orhan [17], Isık et al. ([18],[19],[20]), Kuc¸¨ ukaslan ¨ et al. ([21],[22]), Mursaleen [23], Salat [24], Savas¸ [25], S¸ engul [26] and many others. The order of statistical con- ¨ vergence of a sequence of numbers was given by Gadjiev and Orhan [27] after then statistical convergence of order ? was studied by C¸ olak [28]. By a lacunary sequence we mean an increasing integer sequence ? = (kr) of non-negative integers such that k0 = 0 and hr = (kr ? kr?1) ? ? as r ? ?. The intervals determined by ? will be denoted by Ir = (kr?1, kr] and the ratio kr kr?1 will be abbreviated by qr , and q1 = k1 for convenience. In recent years, lacunary sequences have been studied in ([7],[8],[9],[29],[30],[31],[32], [17],[33],[34])
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    On lacunary statistical convergence of order ? of difference sequences of fractional order
    (Maltepe Üniversitesi, 2019) Aral, Nazlım Deniz; Et, Mikail
    The purpose of this paper is to introduce the concepts of ? ??lacunary statistical convergence of order ? (0 < ? ? 1) with the fractional order of ? and ? ??lacunary strongly convergence of order ? with the fractional order of ?. We establish some connections between ? ??lacunary strongly convergence of order ? and ? ??lacunary statistical convergence of order ?.
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    On pointwise deferred statistical convergence of sequences of fuzzy mappings
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Et, Mikail
    In this study, we introduce the concepts of pointwise deferred statistical convergence and strongly deferred Cesaro ` pointwise summable sequences of fuzzy mappings. Some relations between pointwise deferred statistical convergence and strongly deferred Cesaro pointwise summable sequences of fuzzy mappings are given.
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    On S ? ?(?, A, F)?convergence and strong N? ? (?, A, F)?convergence
    (Sociedade Brasileira de Matemática, 2023) Kandemir, Hacer Şengül; Et, Mikail; Çakallı, Hüseyin
    In this paper, we introduce strong N ? ? (?, A, F)?convergence and S ? ?(?, A, F)?convergence with respect to a sequence of modulus functions and give some connections between strongly N ? ? (?, A, F)?convergent sequences and S ? ?(?, A, F)?convergent sequences for 0 < ? ? ? ? 1.
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    On strong N?p(?)-convergence and S? (?) ?convergence
    (Maltepe Üniversitesi, 2021) Şengül Kandemir, Hacer; Et, Mikail
    In this paper, we introduce the concept of strong ??convergence of order ? ( or N? p (?) ?convergence ) of sequence of real numbers and give some inclusion relations between the set of all ??statistical convergence of order ? and strong N? p (?)-convergence.
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    On wijsman (f, I) ? lacunary statistical convergence of order ?
    (Maltepe Üniversitesi, 2019) Şengül, Hacer; Et, Mikail; Çakallı, Hüseyin
    In this paper we introduce the concepts of Wijsman (f, I) ?lacunary statistical convergence of order ? and Wijsman strongly (f, I) ?lacunary statistical convergence of order ?, and investigated between their relationship.
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    A variation on lacunary quasi Cauchy sequences
    (AMER INST PHYSICS, 2016) Cakalli, Huseyin; Et, Mikail; Sengul, Hacer; Ashyralyev, A; Lukashov, A
    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.