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Öğe A Framework for I*-Statistical Convergence of Fuzzy Numbers(Mdpi, 2024) Tanushri; Ahmad, Ayaz; Esi, AyhanIn this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*-lim in f.Öğe A study of triple sequence spaces in fuzzy anti-normed linear spaces(Univ Nis, Fac Sci Math, 2023) Pandit, Shailendra; Ahmad, Ayaz; Esi, AyhanThe proposed article aims to study some topological properties of triple real sequence spaces with respect to fuzzy-anti-normed linear space (FANLS). In this work the algebra of fuzzy I lambda-limit and fuzzy I lambda-anti limit, where 0 < lambda < 1 and I is an ideal on N3, of triple real sequences along with an interesting example have been studied. Furthermore, the completeness of a special kind of sequence space with respect to fuzzy anti-norm has been examined.Öğe A Study of Triple Sequences Statistical Convergence in Neutrosophic Normed Spaces(Univ Craiova, 2024) Shankar, Hari; Ahmad, Ayaz; Esi, AyhanNeutrosophic logic, probability, and sets are all included in this discipline. The generalization of conventional sets, fuzzy sets, intuitionistic fuzzy sets, and other related ideas is the neutrosophic set theory. It is a mathematical concept that deals with situations involving inconsistent, ambiguous, and imprecise data. To fully understand sequence spaces, statistical convergence is a crucial concept. In this particular scientific work, we introduce the notion of statistical convergence for triple sequences in the neutrosophic normed space. In this neutrosophic normed space, we also explore the statistical properties of completeness and triple Cauchy sequences.Öğe ANALYZING LACUNARY △m-STATISTICAL CONVERGENCE IN NEUTROSOPHIC NORMED SPACES(Amer Inst Mathematical Sciences-Aims, 2026) Shankar, Hari; Ahmad, Ayaz; Chaurasiya, Chandan; Esi, Ayhan. This paper explores the notions of lacunary triangle m-statistical convergence, lacunary triangle m-statistical Cauchy sequences, and lacunary strongly triangle m-convergence within the framework of neutrosophic normed linear spaces (NNLS). We establish the uniqueness of limit and certain algebraic properties of lacunary triangle m-statistical convergence in NNLS, offering a rigorous foundation for these concepts. Additionally, we introduce the concept of strong Ces & aacute;ro summability in NNLS and conduct an in-depth analysis of its properties. The connections between lacunary strong triangle m-convergence and Ces & aacute;ro summability are also examined, revealing significant interrelationships between these two convergence methods.Öğe Assessing the Fuzzy n-Inner Product Spaces and Its Impact on Linear Operators(Soc Paranaense Matematica, 2026) Ahmad, Md Arman; Ahmad, Ayaz; Esi, AyhanFuzzy n-inner product space (f-n-IPS) and its concept induced fuzzy n-normed linear space (f-n-NLS), which generalizes the classical n-inner product spaces to the fuzzy setting, and investigates what effects these generalized fuzzy structures have on the properties of linear operators. We construct a specific f-n-IPS and obtain some fundamental properties that relate the fuzzy inner product to the fuzzy norm. Then, the paper characterizes fuzzy bounded and fuzzy continuous linear operators T : (X, N-1) -> (Y, N-2) between these fuzzy spaces. One of the surprising findings is that, in this fuzzy context, a fuzzy bounded linear operator is always fuzzy continuous; however, the converse may not be true in general, which represents a critical difference from the classic theory of operators. Nevertheless, we prove that in the case when the space X is finite-dimensional, fuzzy continuity yields fuzzy boundedness. Finally, this study generalizes basic concepts from classical operator theory, such as adjoint, self-adjoint, normal, and unitary operators, to this new fuzzy context. With this work, a solid framework for the study of linear operators in imprecise contexts is laid, which provides the possibility for investigation into areas such as fuzzy differential equations and signal processing under uncertainty. Through a rigorous investigation of operator behavior in these uncertain situations, it represents a significant contribution to the growing field of fuzzy mathematics. We provide a basis for possible applications in fuzzy modeling, uncertain signal processing, and multidimensional decision-making systems.Öğe AUTOMATED ASSESSMENT AND OPTIMIZATION OF FUZZY LOGIC IN METRIC SPACE APPLICATIONS(Editura Bibliotheca-Bibliotheca Publ House, 2024) Ahmad, Arman; Ahmad, Ayaz; Esi, Ayhan. In this paper, for fuzzy metric spaces we will attempt to demonstrate some novel fixed-point theorems that is common. To support our findings with evidence, we employ the concept of compatibility. The previous review found several useful mutual fixedpoint theorems for metric and fuzzy metric spaces. Our results greatly expand and strengthen these theorems. Reconsideration of fuzzy metric spaces is done by this study so that fuzzy scalars are utilized to construct fuzzy metric spaces rather than real numbers or fuzzy numbers. In contrast to the preceding work, which defined fuzzy metric spaces using fuzzy or real numbers, this definition uses fuzzy numbers. It has been demonstrated that any complete regular metric space can, under certain conditions, complete fuzzy metric space are given. In addition, we provide evidence that the fuzzy metric spaces generate fuzzy topology that is specified in this study and is consistent with previously presented fuzzy topologies. In the coming years, these findings will pave the way for additional research into imperfect optimization and pattern recognition.Öğe Exploring Bounded Linear Operators in Neutrosophic Normed Linear Spaces(Tsinghua Univ Press, 2025) Chaurasiya, Chandan; Ahmad, Ayaz; Shankar, Hari; Esi, AyhanThis study focuses on analyzing the convergence of the product of sequences and investigating the Cauchy sequences under specific conditions within neutrosophic normed linear spaces (NNLS). Additionally, we define various types of bounded linear operators (both strong and weak) that constitute a linear space, and we explore the concept of neutrosophic compact linear operators.Öğe Monotonicity, boundedness, and convergence for sequences of fuzzy numbers(Univ Nis, Fac Sci Math, 2024) Tanushri; Ahmad, Ayaz; Esi, AyhanWe present the concepts of ideal monotonicity and ideal boundedness in the context of sequences involving fuzzy numbers. Additionally, we formulate an equivalent to the monotone convergence theorem and provide the necessary proofs for decomposition theorems specifically designed for this category of sequences. Our exploration extends to the analysis of I & lowast;-convergent sequences of fuzzy numbers, concluding with the demonstration that these sequences have a unique limit point.Öğe NEUTROSOPHIC FUZZY I-CONVERGENT FIBONACCI DIFFERENCE SEQUENCE SPACES(Amer Inst Mathematical Sciences-Aims, 2025) Chaurasiya, Chandan; Ahmad, Ayaz; Esi, AyhanIn this work, we analyze the Fibonacci difference matrix and use it to develop new sequence spaces in the neutrosophic normed spaces (NNS). This study also includes a detailed analysis of several important properties of these spaces, including their linearity property, first countability and Hausdorffness.Öğe λ-Statistical Pointwise and Uniform Convergence of Sequences of Functions on Neutrosophic Normed Spaces(Univ Maragheh, 2025) Shankar, Hari; Ahmad, Ayaz; Chaurasiya, Chandan; Esi, AyhanThis insightful article examines the A-statistical convergence of function sequences within neutrosophic norm spaces. It introduces novel concepts such as A-statistical pointwise convergence and A-statistical uniform convergence specifically tailored for neutrosophic norm spaces, representing a notable advancement in the field. The article elucidates the foundational properties of these innovative concepts, offering valuable insights into their theoretical foundations and practical applications.
