Papers by Mehmet Küçükaslan
arXiv (Cornell University), Sep 28, 2022
Some types of statistical convergence such as statistical order and deferred statistical converge... more Some types of statistical convergence such as statistical order and deferred statistical convergences have been studied and investigated in Riesz spaces, recently. In this paper, we introduce the concept of deferred statistical convergence in Riesz spaces with order convergence. Moreover, we give some relations between deferred statistical order convergence and other kinds of statistical convergences.
Applied Mathematics E Notes, 2013
The aim of the present paper is to give some properties of A-statistical convergence of sequences... more The aim of the present paper is to give some properties of A-statistical convergence of sequences. We give de…nition of A-statistical monotonicity, upper and lower peak points of sequences. The relation between these concepts and A-statistical monotonicity is investigated. Also, some results given in [11] are generalized.
Ukrainian Mathematical Journal, 2002
We study the rate of convergence of Fourier series of orthogonal polynomials over an area inside ... more We study the rate of convergence of Fourier series of orthogonal polynomials over an area inside and on the closure of regions of the complex plane.
Notes on Intuitionistic Fuzzy Sets, 2018
In this paper, the intuitionistic fuzzy deferred statistical convergence in the intuitionistic fu... more In this paper, the intuitionistic fuzzy deferred statistical convergence in the intuitionistic fuzzy normed space is defined by considering deferred density given in [13]. Besides the main properties of this new method, it is compared with intuitionistic fuzzy statistical convergence and itself under different restrictions on the method. Some special cases of the obtained results are coincided with known results in literature.
Journal of the Indonesian Mathematical Society, 2020
In this paper, by using natural density of subsets of N, the statistical limit and cluster points... more In this paper, by using natural density of subsets of N, the statistical limit and cluster points of the arithmetical functions (ap (n)), γ (n),τ(n), Δ γ (n) and Δ τ (n) are studied. In addition to this, we also investigate statistical limit and cluster points of (Δ r γ (n) and (Δ r τ (n)) for each r ın N.
Let p(n) and q(n) be nondecreasing sequence of positive integers such that p(n) < q(n) and lim... more Let p(n) and q(n) be nondecreasing sequence of positive integers such that p(n) < q(n) and limn→∞ q(n) = ∞ holds. For any r ∈ Z^+, we define D_p,q^+r- statistical convergence of ∆^+r x where ∆^+r is r- th difference of the sequence (x_n). The main results in this paper consist in determining sets of sequences χ and χ' of the form [D_ p^q]_0 α satisfying χ ⊂ [D_p^q]_0(∆^+r ) ⊂ χ ' and sets φ and φ' of the form [D_p^q]_α satisfying φ ≤ [D_p^q]_∞(∆^+r ) ≤ φ' .
Journal of Inequalities and Applications, 2010
The aim of this paper is to investigate approximation properties of some extremal polynomials in ... more The aim of this paper is to investigate approximation properties of some extremal polynomials in A 1 p , p > 0 space. We are interested in finding approximation rate of extremal polynomials to Riemann function in A 1 p and C-norms on domains bounded by piecewise analytic curve. where dσ z is two-dimensional Lebesgue measure. Also, let us denote by ℘ n the class of all polynomials P n z , deg P n ≤ n, with P n z 0 0, P n z 0 1 and consider following extremal problem: G ϕ z − P n z p dσ z −→ min, p > 0. 1.2
For subsets of R^+ = [0,∞) we introduce a notion of coherently porous sets as the sets for which ... more For subsets of R^+ = [0,∞) we introduce a notion of coherently porous sets as the sets for which the upper limit in the definition of porosity at a point is attained along the same sequence. We prove that the union of two strongly porous at 0 sets is strongly porous if and only if these sets are coherently porous. This result leads to a characteristic property of the intersection of all maximal ideals containing in the family of strongly porous at 0 subsets of R^+. It is also shown that the union of a set A ⊆ R^+ with arbitrary strongly porous at 0 subset of R^+ is porous at 0 if and only if A is lower porous at 0.
Let B_1(Ω, R) be the first Baire class of real functions in the pluri-fine topology on an open se... more Let B_1(Ω, R) be the first Baire class of real functions in the pluri-fine topology on an open set Ω⊆ C^n and let H_1^*(Ω, R) be the first functional Lebesgue class of real functions in the same topology. We prove the equality B_1(Ω, R)=H_1^*(Ω, R) and show that for every f∈ B_1(Ω, R) there is a separately continuous function g: Ω^2→ R in the pluri-fine topology on Ω^2 such that f is the diagonal of g.
We investigate the interrelations between labeled trees and ultrametric spaces generated by these... more We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics, and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.
arXiv: General Topology, 2015
Let $B_{1}(\Omega, \mathbb R)$ be the first Baire class of real functions in the pluri-fine topol... more Let $B_{1}(\Omega, \mathbb R)$ be the first Baire class of real functions in the pluri-fine topology on an open set $\Omega \subseteq \mathbb C^{n}$ and let $H_{1}^{*}(\Omega, \mathbb R)$ be the first functional Lebesgue class of real functions in the same topology. We prove the equality $B_{1}(\Omega, \mathbb R)=H_{1}^{*}(\Omega, \mathbb R)$ and show that for every $f\in B_{1}(\Omega, \mathbb R)$ there is a separately continuous function $g: \Omega^{2} \to\mathbb R$ in the pluri-fine topology on $\Omega^2$ such that $f$ is the diagonal of $g.$
arXiv: Metric Geometry, 2012
Let A ⊆ C be a starlike set with a center a. We prove that every tangent space to A at the point ... more Let A ⊆ C be a starlike set with a center a. We prove that every tangent space to A at the point a is isometric to the smallest closed cone, with the vertex a, which includes A. A partial converse to this result is obtained. The tangent space to convex sets is also discussed.
Annales Academiae Scientiarum Fennicae Mathematica, 2017
Let M be a class of metric spaces. A metric space Y is minimal M-universal if every X ∈ M can be ... more Let M be a class of metric spaces. A metric space Y is minimal M-universal if every X ∈ M can be isometrically embedded in Y but there are no proper subsets of Y satisfying this property. We find conditions under which, for given metric space X, there is a class M of metric spaces such that X is minimal M-universal. We generalize the notion of minimal M-universal metric space to notion of minimal M-universal class of metric spaces and prove the uniqueness, up to an isomorphism, for these classes. The necessary and sufficient conditions under which the disjoint union of the metric spaces belonging to a class M is minimal M-universal are found. Examples of minimal universal metric spaces are constructed for the classes of the three-point metric spaces and n-dimensional normed spaces. Moreover minimal universal metric spaces are found for some subclasses of the class of metric spaces X which possesses the following property. Among every three distinct points of X there is one point lying between the other two points.
Journal of Inequalities and Applications, 2015
The deferred Cesáro transformation, which has useful properties not possessed by the Cesáro trans... more The deferred Cesáro transformation, which has useful properties not possessed by the Cesáro transformation, was considered by RP Agnew in 1932. The aim of this paper is to give a generalization of deferred Cesáro transformations by taking account of some well-known transformations and to handle some of their properties as well. On the other hand, we shall consider the approximation by the generalized deferred Cesáro means in a generalized Hölder metric and present some applications of the approach concerning some sequence classes.
Ukrainian Mathematical Journal, 2014
We study the statistical convergence of metric valued sequences and of their subsequences. The in... more We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Annales Academiae Scientiarum Fennicae Mathematica, 2011
We find necessary and sufficient conditions for an arbitrary metric space X to have a unique pret... more We find necessary and sufficient conditions for an arbitrary metric space X to have a unique pretangent space at a marked point a ∈ X. Applying this general result we show that each logarithmic spiral has a unique pretangent space at the asymptotic point. Unbounded multiplicative subgroups of C * = C \ {0} having unique pretangent spaces at zero are characterized as lying either on the positive real semiaxis or on logarithmic spirals. Our general uniqueness conditions in the case X ⊆ R make it also possible to characterize the points of the ternary Cantor set having unique pretangent spaces.
We find necessary and sufficient conditions under which an arbitrary metric space X has a unique ... more We find necessary and sufficient conditions under which an arbitrary metric space X has a unique pretangent space at the marked point a ∈ X.
In this work, statistical boundedness is defined in a metric space and, statistical boundedness ... more In this work, statistical boundedness is defined in a metric space and, statistical boundedness of metric valued sequences and their subsequences are studied. The interplay between the statistical boundedness and boundedness in a metric spaces are also studied, and it is shown that boundedness imply statistical boundedness and if the number of elements of the metric space is finite then these two concepts coincide. Moreover, here is given analogy of Balzano-Weierstrass Theorem.
Journal of the Indonesian Mathematical Society
By using modulus functions, we have obtained a generalization of statistical convergence of asymp... more By using modulus functions, we have obtained a generalization of statistical convergence of asymptotically equivalent sequences, a new non-matrix convergence method, which is intermediate between the ordinary convergence and the statistical convergence. Further, we have examined some inclusion relations related to this concept.
TURKISH JOURNAL OF MATHEMATICS, 2017
For subsets of R + = [0, ∞) we introduce a notion of coherently porous sets as the sets for which... more For subsets of R + = [0, ∞) we introduce a notion of coherently porous sets as the sets for which the upper limit in the definition of porosity at a point is attained along the same sequence. We prove that the union of two strongly porous at 0 sets is strongly porous if and only if these sets are coherently porous. This result leads to a characteristic property of the intersection of all maximal ideals contained in the family of strongly porous at 0 subsets of R +. It is also shown that the union of a set A ⊆ R + with arbitrary strongly porous at 0 set is porous at 0 if and only if A is lower porous at 0 .
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Papers by Mehmet Küçükaslan