Lacunary Statistical Convergence of Double Sequences in Fuzzy Paranormed Spaces

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Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi
Cilt: 26 Sayı: 1
Lacunary Statistical Convergence of Double Sequences in Fuzzy Paranormed Spaces

Lacunary Statistical Convergence of Double Sequences in Fuzzy Paranormed Spaces

Authors : Muhammed Recai Türkmen

Pages : 50-56

Doi:10.35414/akufemubid.1714565

View : 59 | Download : 69

Publication Date : 2026-01-19

Article Type : Research Paper

Abstract :This article introduces the concept of lacunary statistical convergence for double sequences in fuzzy–paranormed spaces. We first define fp–lacunary statistically convergent and fp–lacunary Cauchy double sequences, then establish their fundamental properties, uniqueness of limits, linearity under addition and scalar multiplication, and the Cauchy criterion. Next, we examine how these properties interact under the structural features of lacunary schemes and fuzzy–paranormed spaces. Finally, we present algebraic theorems for double. Our results demonstrate that the characteristic behaviors of lacunary sequences are preserved within fuzzy–paranormed spaces, which combine both fuzzy–normed and paranormed structures.
Keywords : fuzzy paranorm, çift diziler, lacunary yakınsama, İstatistiksel yakınsama, Cauchy

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