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    Introducing n-sequences and study of their topological properties
    (Semnan Univ, 2022) Tabassum, Sabiha; Fatma, Ruqaiyya; Esi, Ayhan
    In this article, the concept of n-sequences in topological spaces has been introduced which is new to the existing literature. We study the sequential limit aspect of statistical convergence for such sequences. Besides, the notions of subsequences, limit points, statistical limits points, and statistical cluster points in topological spaces have been given for n-sequences. This material contains a detailed explanation of inclusion relations between these points spaces and their basic properties. We also introduce s(n), and s(n)*-convergent spaces and discuss some of their properties.
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    $q$-Cesaro Summable Sequences Defined by Orlicz Function
    (Mehmet Zeki SARIKAYA, 2026) Tabassum, Sabiha; Kumar, Praveen; Esi, Ayhan
    [Abstract Not Available]
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    q-Cesàro Summable Sequences Defined by Orlicz Function
    (Prof. Dr. Mehmet Zeki SARIKAYA, 2026) Tabassum, Sabiha; Kumar, Praveen; Esi, Ayhan
    This paper introduces and systematically investigates the sequence spaces defined by the combination of q-calculus, statistical convergence, and Orlicz functions. We begin by defining the concept of q-statistical convergence with respect to an Orlicz function M, denoted by SMq. Furthermore, we introduce the notion of q-strong summability w.r.t an Orlicz function M, denoted by WMq. We establish several inclusion relations between the spaces SMq and WMq and other classical sequence spaces. We prove that, under suitable conditions, both SMq and WMq are linear spaces. © 2026, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.
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    q-statistical convergence of double sequences of order λ
    (Univ Nis, Fac Sci Math, 2025) Tabassum, Sabiha; Al Amodi, Noor Ali Ahmed Abdullah; Esi, Ayhan
    The quantum calculus or a q-calculus is the generalization as well as modifications of the classical calculus. Over the last twenty years, the subject of q-calculus has served as a connection between mathematics and physics. In recent past there is a substantial increase of research in field of q-calculus because of its applications in many fields such as number theory, combinatorics, special functions basic hyper geometric functions mechanics, theory of relativity and other sciences-quantum theory. In this paper we introduce the concept of q-analoge of statistical convergence of double sequence of order lambda and studied some of its geometric properties. Further, we define q-cesa`ro summability of order lambda and gave the relationship between q-strong p-cesa`ro summability of order lambda and the q-statistical convergence of double sequences of order mu for lambda <= mu.