Results 81 to 90 of about 1,622,947 (195)
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 +2 more
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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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?-statistical convergent double lacunary sequence spaces
, 2015 In the present paper we introduce mu-statistical convergent double lacunary sequence spaces defined by a sequence of Orlicz function M = (M-kl) over n-normed spaces.
Esi, Ayhan, Sharma, S. K.
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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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Journal of Function Spaces, 2018 We first define the notion of lacunary statistical convergence of order (α,β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M=(Mk) of ...
S. A. Mohiuddine +2 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
wiley +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
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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 +2 more
wiley +1 more source
SOME DOUBLE LACUNARY SEQUENCE SPACES
, 2014 The purpose of this paper is to introduce some double lacunary sequence spaces defined by a sequence of Orlicz functions. We also make an effort to study some topological properties and inclusion relations between these sequence ...
Sharma, Sunil K. +2 more
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