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    A characterization of h-strongly porous subsets of R
    (Univ Nis, Fac Sci Math, 2024) Altinok, Maya; Kucukaslan, Mehmet
    In this paper, notion of h-porosity of the subsets of real numbers at zero is investigated. Then, a characterization for h-strongly porous subsets of real numbers is given.
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    A RELATION BETWEEN POROSITY CONVERGENCE AND PRETANGENT SPACES
    (Publications L Institut Mathematique Matematicki, 2021) Altinok, Maya; Kucukaslan, Mehmet
    The convergence of porosity is one of the relatively new concept in Mathematical analysis. It is completely structurally different from the other convergence concepts. Here we give a relation between porosity convergence and pretangent spaces.
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    Convergence of measurable functions in the sense of density
    (Springernature, 2023) Altinok, Maya; Kucukaslan, Mehmet; Unay, A. Kerem
    In this paper, by using unbounded modulus function the notion mu(f)-density for measurable subsets of I = [1, infinity] is defined and related notion mu f-statistical convergence of measurable functions is investigated. In addition to the basic properties of mu(f)-density and mu(f)-statistical convergence, the definition of being mu(f)-Cauchy is given and it is shown that these two concepts are equivalent for real valued measurable functions. Among others, the notion of f-strongly Cesaro summability is introduced. Finally, necessary and sufficient conditions between f-strongly Cesaro summability and mu(f)-statistical convergence are given under explicated restrictions on measurable function and modulus function.
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    On Asymptotically Wijsman Deferred Statistical Equivalence of Sequence of Sets
    (Chiang Mai Univ, Fac Science, 2020) Altinok, Maya; Inan, Burcu; Kucukaslan, Mehmet
    The concept of Wijsman deferred statistical convergence of sequences of sets was defined by authors in [M. Altinok, B. Inan, M. Kucukaslan, On deferred statistical convergence of sequences of sets in Metric space, TJMCS. (2015)]. In this paper, by considering this notation asymptotically Wijsman deferred statistical equivalence of sequences of sets is defined. Besides main properties of asymptotically Wijsman deferred statistical equivalence, some inclusion results are given under strict restrictions. The obtained theorems include some known results in literature.
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    STATISTICAL EXTENSION OF BOUNDED SEQUENCE SPACE
    (Ankara Univ, Fac Sci, 2021) Altinok, Maya; Kucukaslan, Mehmet; Kaya, Umutcan
    In this paper by using natural density real valued bounded sequence space l(infinity) is extented and statistical bounded sequence space l(infinity)(st) is obtained. Besides the main properties of the space l(infinity)(st), it is shown that l(infinity)(st) is a Banach space with a norm produced with the help of density. Also, it is shown that there is no matrix extension of the space l(infinity) that its bounded sequences space covers l(infinity)(st). Finally, it is shown that the space l(infinity) is a non-porous subset of l(infinity)(st).
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    WEIGHTED STATISTICAL CONVERGENCE OF REAL VALUED SEQUENCES
    (Univ Nis, 2020) Adem, Abdu Awel; Altinok, Maya
    Functions defined in the form g : N -> [0, infinity) such that lim(n ->infinity) g(n) = infinity and lim(n ->infinity) n/g(n) = 0n are called weight functions. Using the weight function, the concept of weighted density, which is a generalization of natural density, was defined by Balcerzak, Das, Filipczak and Swaczyna in the paper \Generalized kinsd of density and the associated ideals, Acta Mathematica Hungarica 147(1) (2015), 97-115. In this study, the definitions of g-statistical convergence and g-statistical Cauchy sequence for any weight function g are given and it is proved that these two concepts are equivalent. Also, some inclusions of the sets of all weight g(1)-statistical convergent and weight g(2)-statistical convergent sequences for g(1), g(2) which have the initial conditions are given.