Yazar "Debnath, Shyamal" seçeneğine göre listele

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    A new notion of convergence in gradual normed linear spaces
    (Institute of Mathematics, 2024) Choudhury, Chiranjib; Debnath, Shyamal; Esi, Ayhan
    In this paper we introduce the notion of Iλ −statistical convergence of sequences as one of the extensions of I− statistical convergence in the gradual normed linear spaces. We investigate some fundamental properties of the newly introduced notion and its relationship with I− statistical convergence. In the end, we introduce and investigate the concept of Iλ −statistical limit points, cluster points and establish some implication relations. © 2024, Institute of Mathematics. All rights reserved.
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    Asymptotically double λ2-statistically equivalent sequences of interval numbers
    (Editura Academiei Române, 2020) Esi, Ayhan; Debnath, Shyamal; Saha, Subrata
    In this paper we have introduced the concept of ?2-asymptotically double statistical equivalent of interval numbers and strong ?2-asymptotically double statistical equivalent of interval numbers. We have investigated the rela-tions related to these spaces. © 2020, Publishing House of the Romanian Academy. All rights reserved.
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    Further results on I-deferred statistical convergence
    (Univ Nis, Fac Sci Math, 2024) Choudhury, Chiranjib; Debnath, Shyamal; Esi, Ayhan
    For a non-empty set X, an ideal I represents a family of subsets of X that is closed under taking finite unions and subsets of its elements. Considering X = N, in the present study, we set forth with the new notion of I-deferred statistical limit point, I-deferred statistical cluster point and study various properties of the newly introduced notion. For a real valued sequence x = (xn), we prove that every I-deferred statistical limit point is an I-deferred statistical cluster point. Moreover, the collection of all I-deferred statistical cluster points of x is a closed subset of R. We also introduce the notion of I-deferred statistical limit superior and inferior for real valued sequences and prove several interesting properties. In the end, we establish a necessary and sufficient condition under which a I-deferred statistically bounded real valued sequence is I-deferred statistically convergent.
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    On extremal rough i-convergence limit point of triple sequence spaces defined by a metric function
    (Korean Society for Computational and Applied Mathematics, 2020) Subramanian, Nagarajan; Esi, Ayhan; Debnath, Shyamal
    We introduce and study some basic properties of rough I-convergent of triple sequence spaces and also study the set of all rough I-limits of a triple sequence spaces.
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    On I-statistical convergence of complex uncertain sequences
    (Univ Nis, Fac Sci Math, 2024) Halder, Amit; Debnath, Shyamal; Esi, Ayhan
    The concept of I- statistical convergence almost surely of complex uncertain sequences was introduced by Halder and Debnath, which is a very recent and new approach in complex uncertainty theory. Based on that technique, in this article, we introduced the concept of I- statistical convergence in mean, distribution, uniformly almost surely of complex uncertain sequence. Also, we explore the concept of I- statistical convergence in p-distance, completely I- statistical convergence, and I- statistical convergence in metric of complex uncertain sequences. Overall, this study mainly presents a complete diagrammatic scenario of interrelationships among all I- statistical convergence concepts of complex uncertain sequences and include some observations about the above convergence concepts.