Results 81 to 90 of about 1,546,174 (193)

Discatenated and lacunary recurrences [PDF]

Notes on Number Theory and Discrete Mathematics
Recursive sequences with gaps have been studied previously. This paper considers some elementary properties of such sequences where the gaps have been created on a regular basis from sequence to sequence – ‘discatenated’ (systematic gaps) and ‘lacunary’
Hakan Akkuş, Ömür Deveci, Engin Özkan, Anthony G. Shannon   +3 more
doaj   +1 more source

On strongly I and I*-lacunary convergence of sequences of sets [PDF]

AIP Conference Proceedings, 2014
In this paper we study the concepts of Wijsman strongly lacunary convergence, Wijsman strongly I-lacunary convergence, Wijsman strongly I*-lacunary convergence and Wijsman strongly I-lacunary Cauchy sequences of sets and investigate the relationship between them.
Sever, Yurdal, Ulusu, Uğur, Dündar, Erdinç   +2 more
openaire   +4 more sources

Strongly Lacunary Ideal Convergence of Sequences of Functions

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In the present paper, we introduce the notions of strongly lacunary convergence, strongly lacunary I‐convergence, and strongly lacunary I∗‐convergence for sequences of functions, while analyzing the interrelations among these established concepts. Furthermore, we formulate the definitions of strongly lacunary I‐Cauchy and strongly lacunary I∗‐Cauchy ...
Nimet Akın, Erdinç Dündar, Claudia Capone   +2 more
wiley   +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

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, Taja Yaying, Orhan Tuğ, Ömer Kisi, Qing-Bo Cai, Nikhil Khanna   +5 more
wiley   +1 more source

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
openaire   +4 more sources

Wijsman Statistical, Strong Cesàro, and Ideal Convergence of Closed Sets in Idempotent Bicomplex Metric Spaces

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, Mehmet Gürdal, Ömer Kişi, Abdelwaheb Mhemdi, Maria Alessandra Ragusa   +4 more
wiley   +1 more source

Strongly lacunary delta ward continuity [PDF]

, 2015
International Conference on Advancements in Mathematical Sciences (AMS) -- NOV 05-07, 2015 -- Antalya, TURKEYIn this paper, the concepts of a lacunary statistically delta-quasi-Cauchy sequence and a strongly lacunary delta-quasiCauchy sequence are ...
Huseyin Kaplan, Huseyin Cakalli, Cakalli, Huseyin, Kaplan, Huseyin   +3 more
core   +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

Lacunary strong $(A_\sigma, p)$-convergence

, 2005
summary:The definition of lacunary strongly convergence is extended to the definition of lacunary strong $(A_{\sigma }, p)$-convergence with respect to invariant mean when $A$ is an infinite matrix and $p = (p_i)$ is a strictly positive sequence.
Bilgin, Tunay
core   +1 more source