Results 61 to 70 of about 211 (159)
The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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On the fractional parts of lacunary sequences
MATHEMATICA SCANDINAVICA, 2006 In this paper, we prove that if $t_0, t_1, t_2, \dots$ is a lacunary sequence, namely, $t_{n+1}/t_n\geq 1+r^{-1}$ for each $n\geq 0$, where $r$ is a fixed positive number, then there are two positive constants $c(r)=\max(1-r, 2(3r+6)^{-2})$ and $\xi=\xi(t_0, t_1,\dots)$ such that the fractional parts $\{\xi t_n\}$, $n=0,1,2,\dots$, all belong to a ...
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Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order
International Journal of Mathematics and Mathematical Sciences, 2015 We generalize the lacunary statistical convergence by introducing the generalized difference operator Δνα of fractional order, where α is a proper fraction and ν=(νk) is any fixed sequence of nonzero real or complex numbers.
Ugur Kadak
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Variations on lacunary statistical quasi Cauchy sequences [PDF]
AIP Conference Proceedings, 2019 In this paper, we introduce a concept of lacunary statistically p-quasi-Cauchyness of a real sequence in the sense that a sequence (αk) is lacunary statistically p-quasi-Cauchy if limr→∞1hr|{k ∈ Ir:|αk+p−αk|≥e}| = 0 for each e > 0. A function f is called lacunary statistically p-ward continuous on a subset A of the set of real numbers ℝ if it preserves
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Some Paranormed Sequence Spaces Which Involve Arithmetic Divisor Sum Function
Journal of Function Spaces, Volume 2026, Issue 1, 2026.Let Dr, r ≥ 0, be a triangle and q = (qj) be a bounded sequence of strictly positive numbers. In this paper, we study the algebraic and topological properties of the paranormed sequence space ℓDr,q, generated by the triangle Dr over Maddox′s space ℓ(q). We identify the Schauder basis as well as the α‐, β‐, and γ‐duals of the space ℓDr,q. One section is
Ting Gan +5 more
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ITM Web of Conferences, 2018 The notion of the α th order Δim - lacunary statistical convergence and α th order lacunary strongly (Δim, p)-summable sequences was introduced by Altınok et al. [1].
Et Mikail +2 more
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.This paper studies generalized Wijsman convergence for sequences of nonempty closed subsets of an idempotent bicomplex metric space. Let ρ = d1e1 + d2e2, where d1 and d2 are metrics on the same underlying set X. For a nonempty subset A of X, we define the bicomplex point‐to‐set distance by ρ(x, A) = d1(x, A)e1 + d2(x, A)e2.
Ameni Gargouri +4 more
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Diagonal Window Tests for Deferred Weighted Frequent Cauchy Sequences and Mean Coherence
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper studies when a diagonal pairwise sampling condition of pre‐Cauchy type can be upgraded to a genuine convergence criterion in the deferred weighted setting. Working with the window system determined by (λ, μ), we introduce a diagonal pairwise framework and compare it with the corresponding two‐parameter Pringsheim measure on N×N.
Ameni Gargouri +4 more
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Variations on strong lacunary quasi-Cauchy sequences
Journal of Nonlinear Sciences and Applications, 2016 We introduce a new function space, namely the space of Nθ (p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. Nθα(p)-ward continuity is also introduced and investigated for any fixed 0 < α ≤ 1, and for any fixed positive integer p. A real valued function f defined on a
Kaplan, Huseyin, Cakalli, Huseyin
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Lacunary statistical convergence and inclusion properties between lacunary methods
International Journal of Mathematics and Mathematical Sciences, 2000 A lacunary sequence is an increasing integer sequence θ={kr} such that kr−kr−1→∞ as r→∞. A sequence x is called sθ-convergent to L provided that for each ϵ>0, limr(1/(kr−kr−1)){the number of kr ...
Jinlu Li
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