Triple Lacunary Sequence Spaces for Fuzzy Numbers

Abstract

It was Nanda [29] in 1989 who demonstrate that all convergent fuzzy number sequences are complete metric spaces. Nuray [30] gave the relations between lacunary statistical convergent and statistical convergent sequences in fuzzy numbers. Various aspects of fuzzy number sequences have been discussed by many different authors. In this work, we peruse the notions of lacunary statistical convergence of a triple sequence of fuzzy numbers and triple lacunary strongly p-Cesàro summability. We define triple lacunary statistically Cauchy sequence, triple lacunary strongly p-Cesàro summable and lacunary statistically convergent to a fuzzy number. We think that there is a relationship between these various concepts. Thus in this article, we include some basic theorems on this subject.

Keywords

• Lacunary statistical convergence
• Statistical convergence
• Fuzzy number
• Triple sequence

Bulanık Sayılar için Üç İndisli Lacunary Dizi Uzayları

Abstract

Nanda [29] 1989 yılında bütün yakınsak bulanık sayı dizilerinin tam metrik uzaylar olduğunu gösterdi. Ayrıca, Nuray [30] bulanık sayılarda lacunary istatistiksel yakınsak ve istatistiksel yakınsak diziler arasındaki ilişkileri verdi. Bununla birlikte, bulanık sayı dizilerinin çeşitli yönleri birçok yazar tarafından tartışılmıştır. Bu çalışmada, üç indisli bir bulanık sayı dizisinin lacunary istatistiksel yakınsaklığı ve üç indisli lacunary güçlü p-Cesàro toplanabilmesi kavramları incelenmiştir. Üç indisli lacunary istatistiksel Cauchy dizisi, üç indisli lacunary güçlü p-Cesàro toplanabilme ve lacunary istatistiksel olarak bulanık bir sayıya yakınsak olmayı tanımlıyoruz. Bu çeşitli kavramlar arasında bir ilişki olduğunu düşünüyoruz ve bu nedenle, makalede bu konu ile ilgili bazı temel teoremlere yer veriyoruz.

Keywords

• Lacunary istatistiksel yakınsaklık
• İstatistiksel yakınsaklık
• Bulanık sayı
• Üç indisli dizi

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