Results 41 to 50 of about 161 (125)
Lacunary statistical convergence and strongly lacunary summable functions of order α
Filomat, 2017 Summary: The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order \(\alpha\) and lacunary statistical convergence of order \(\alpha\) of real-valued functions which are measurable (in the Lebesgue sense) in the interval \((1, \infty)\). Some relations between lacunary statistical convergence of
Srivastava, H. M., Et, Mikail
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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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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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A Generalization of Lacunary Equistatistical Convergence of Positive Linear Operators
Abstract and Applied Analysis, 2013 In this paper we consider some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence. In particular we study lacunary equi-statistical convergence of approximating operators on spaces, the spaces of all real valued ...
Yusuf Kaya, Nazmiye Gönül
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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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Weighted modulus Sθ-convergence of order α in probability
Arab Journal of Mathematical Sciences, 2017 Let θ={kr}r∈N∪{0} be a lacunary sequence, ϕ be a modulus function and {tn}n∈N be a sequence of real numbers such that tn>δ,∀n∈N (where δ is a fixed positive real number) and Tn=t1+t2+⋯+tn (where n∈N and T0=0).
Sanjoy Ghosal +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
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Modulated Lacunary Statistical and Strong-Cesàro Convergences
Symmetry, 2023 Here, we continued the studies initiated by Vinod K. Bhardwaj and Shweta Dhawan which relate different convergence methods involving the classical statistical and the classical strong Cesàro convergences by means of lacunary sequences and measures of density in N modulated by a modulus function f.
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Lacunary d-statistical convergence and lacunary d-statistical boundedness in metric spaces [PDF]
AIP Conference Proceedings, 2019 In this study, using a lacunary sequence we introduce the concepts of lacunary d−statistically convergent sequences and lacunary d−statistically bounded sequences in general metric spaces.
Hacer Sengul, Mikail Et, Huseyin Cakalli
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On Some New Sequence Spaces and Statistical Convergence Methods for Double Sequences
Demonstratio Mathematica, 2014 In this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences.
Belen Cemal, Yildirim Mustafa
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