Results 61 to 70 of about 200 (156)

On some aspects of lacunary I $\mathcal{I}$ -statistical convergence and its applications in approximation theory via power series method

Journal of Inequalities and Applications
This paper introduces and systematically explores the notion of deferred I $\mathcal{I}$ -lacunary statistical convergence and strongly deferred I $\mathcal{I}$ -lacunary Cesàro convergence for sequences of real numbers, unifying deferred intervals ...
Xiu-Liang Qiu, Humma Javed Sheikh, Kuldip Raj, Qing-Bo Cai   +3 more
doaj   +1 more source

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, Mehmet Gürdal, Ömer Kişi, Abdelwaheb Mhemdi, Smritijit Sen   +4 more
wiley   +1 more source

Quasi-Almost Lacunary Statistical Convergence of Sequences of Sets

International Journal of Analysis and Applications, 2018
In this study, we defined concepts of Wijsman quasi-almost lacunary convergence, Wijsman quasi-strongly almost lacunary convergence and Wijsman quasi q-strongly almost lacunary convergence.
Esra Gulle, Ugur Ulusu
doaj   +2 more sources

Extremal discrepancy behavior of lacunary sequences [PDF]

Monatshefte für Mathematik, 2014
In 1975 Walter Philipp proved the law of the iterated logarithm (LIL) for the discrepancy of lacunary sequences: for any sequence $(n_k)_{k \geq 1}$ satisfying the Hadamard gap condition $n_{k+1} / n_k \geq q > 1,~k \geq 1,$ we have $$ \frac{1}{4 \sqrt{2}} \leq \limsup_{N \to \infty} \frac{N D_N(\{ n_1 x \}, \dots, \{n_N x\})}{\sqrt{2 N \log \log N}}
Aistleitner, Christoph, Fukuyama, Katusi
openaire   +3 more sources

A pointwise ergodic theorem along return times of rapidly mixing systems

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3730-3748, December 2025.
Abstract We introduce a new class of sparse sequences that are ergodic and pointwise universally L2$L^2$‐good for ergodic averages; that is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions.
Sebastián Donoso, Alejandro Maass, Vicente Saavedra‐Araya   +2 more
wiley   +1 more source

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
doaj   +1 more source

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 ...
openaire   +2 more sources

Surface‐Exposed Pd Nanocluster Confined within a Ring‐Shaped Polyoxometalate for Selective Hydrogenation

Advanced Science, Volume 12, Issue 38, October 13, 2025.
A small Pd nanocluster is successfully prepared within a ring‐shaped polyoxometalate via a mild solid‐state reduction process. The resulting surface‐exposed Pd nanocluster functions as a robust heterogeneous reusable catalyst, enabling highly chemoselective hydrogenation of substrates containing multiple reducible functional groups via selective ...
Rui Xi, Kentaro Yonesato, Takafumi Yatabe, Yoshihiro Koizumi, Soichi Kikkawa, Seiji Yamazoe, Koji Harano, Kazuya Yamaguchi, Kosuke Suzuki   +8 more
wiley   +1 more source

Lacunary Statistical Convergence of Order alpha and Lacunary Strongly Summable Sequences of Order alpha of Generalized Difference Sequences

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, Şengül Hacer, Çınar Muhammed   +2 more
doaj   +1 more source

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
openaire   +5 more sources