<p>In this paper, we introduce and investigate new classes of Hilbert ideal convergent Fibonacci difference sequence spaces within the framework of intuitionistic fuzzy normed spaces. By combining the Hilbert matrix with Fibonacci difference operators, the concept of Hilbert <i>I</i>-convergence is extended to the intuitionistic fuzzy setting. Several fundamental algebraic and topological properties of the proposed spaces are established, including linearity, first countability, and the Hausdorff property. Moreover, it is shown that Hilbert ideal convergence is equivalent to Hilbert ideal Cauchy convergence with respect to intuitionistic fuzzy norms. The results obtained in this work generalize a number of existing convergence concepts and provide a unified framework for further studies involving matrix transformations and fuzzy sequence spaces.</p>

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Hilbert ideal convergent Fibonacci difference sequence spaces in intuitionistic fuzzy normed spaces

  • Abdullah A. H. Makharesh,
  • Vakeel A. Khan,
  • Mohammad Arshad,
  • Ayhan Esi

摘要

In this paper, we introduce and investigate new classes of Hilbert ideal convergent Fibonacci difference sequence spaces within the framework of intuitionistic fuzzy normed spaces. By combining the Hilbert matrix with Fibonacci difference operators, the concept of Hilbert I-convergence is extended to the intuitionistic fuzzy setting. Several fundamental algebraic and topological properties of the proposed spaces are established, including linearity, first countability, and the Hausdorff property. Moreover, it is shown that Hilbert ideal convergence is equivalent to Hilbert ideal Cauchy convergence with respect to intuitionistic fuzzy norms. The results obtained in this work generalize a number of existing convergence concepts and provide a unified framework for further studies involving matrix transformations and fuzzy sequence spaces.