Yazar "Cakalli, Hüseyin" seçeneğine göre listele

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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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    Neutrosophic compactness via summability and sequential definitions of connectedness in neutrosophic spaces
    (Univ Nis, Fac Sci Math, 2023) Açıkgöz, Ahu; Cakalli, Hüseyin; Esenbel, Ferhat
    In this study, using the concept of the neutrosophic method introduced earlier, as done in different types of topological spaces, a new type of sequential compactness is introduced and investigated. After giving various definitions which constitute the cornerstones of our research, in the third section, a new perspective to the concept of connectedness is brought, which is among the most important characters of the topology world, based on the concept of the neutrosophic method. By giving examples of each new definition given in the second and third sections, a better understanding of the new concepts given is provided.
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    On G-Compactness of Topological Groups with Operations
    (Univ Nis, Fac Sci Math, 2022) Mucuk, Osman; Cakalli, Hüseyin
    One can notice that if X is a Hausdorff space, then limits of convergent sequences in X give us a function denoted by lim from the set of all convergent sequences in X to X. This notion has been extended by Connor and Grosse-Erdmann to an arbitrary linear functional G defined on a subspace of the vector space of real numbers. Following this idea some authors have defined concepts of G-continuity, G-compactness and G-connectedness in topological groups. In this paper we present some results about G-compactness of topological group with operations such as topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras and many others.
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    Statistically quasi Cauchy sequences in abstract metric spaces
    (Amer Inst Physics, 2019) Sönmez, Ayşe; Cakalli, Hüseyin
    In this extended abstract, we introduce a concept of statistically quasi-Cauchyness of a sequence in X in the sense that a sequence (x(k)) is statistically quasi -Cauchy in X if lim(n ->infinity) 1/n vertical bar{k <= n : d(x(k+1), x(k)) - c is an element of P}vertical bar for each c is an element of P where (X, d) is a cone metric space, and p denotes interior of a cone P of X. It turns out that a function f from a totally bounded subset A of X into X is uniformly continuous if f preserves statistically quasi-Cauchy sequences.
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    STRONGLY LACUNARY CONVERGENCE OF ORDER ? IN NEUTROSOPHIC NORMED SPACES
    (Ivane Javakhishvili Tbilisi State Univ, 2023) Kandemir, H. S.; Mikail, Et; Cakalli, Hüseyin
    In this paper, the concept of a strongly lacunary convergence of order a in the neu-trosophic normed spaces is introduced. A few fundamental properties of this new concept are investigated.
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    Variations on Rho statistical quasi Cauchy sequences
    (AIP Publishing, 2019) Cakalli, Hüseyin
    A sequence (?k) of points in R, the set of real numbers, is called ?-statistically p quasi Cauchy if lim n?? 1 ?n |{k ? n : |?p?k | ? ?}| = 0 for each ? > 0, where ? = (?n) is a non-decreasing sequence of positive real numbers tending to ? such that lim supn ?n n < ?, ??n = O(1), and ?p?k+p = ?k+p ? ?k for each positive integer k, p is a fixed positive integer. A real-valued function defined on a subset of R is called ?-statistically p-ward continuous if it preserves ?-statistical p-quasi Cauchy sequences. We obtain results related to ?-statistical p-ward continuity, ?-statistical p-ward compactness, p-ward continuity, ward continuity, and uniform continuity.
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    WEIGHTED STATISTICAL CONVERGENCE OF ORDER a OF DIFFERENCE SEQUENCES
    (Univ Nis, 2023) Kandemir, Hacer Şengül; Et, Mikail; Cakalli, Hüseyin
    Study of difference sequences is a recent development in the summability theory. Sometimes a situation may arise that we have a sequence at hand and we are interested in sequences formed by its successive differences and in the structure of these new sequences. Studies on difference sequences were introduced in the 1980s and after that many mathematicians studied these kind of sequences and obtained some generalized difference sequence spaces. In this study, we generalize the concepts of weighted statistical convergence and weighted ([Np]) over bar -summability of real (or complex) numbers sequences to the concepts of Delta(m)-weighted statistical convergence of order alpha and weighted [(Np) over bar (alpha)] (Delta(m), r)-summability of order alpha by using generalized difference operator Delta(m) and examine the relationships between Delta(m)-weighted statistical convergence of order alpha and weighted [(Np) over bar (alpha)] (Delta(m), r)-summability of order alpha. Our results are more general than the corresponding results in the existing literature.