<p>In this paper, we focus on the notion of sliding window statistical convergence of generalized fractional difference sequences by introducing the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Delta^{a,b,c}_{_{\varrho, \vartheta}}(\mu)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mi mathvariant="normal">Δ</mi> <mmultiscripts> <mrow /> <mrow> <mi>ϱ</mi> <mo>,</mo> <mi>ϑ</mi> </mrow> <mrow /> </mmultiscripts> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> </mrow> </mmultiscripts> <mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-convergence, which extends classical notions of convergence of fractional difference sequences to accommodate the unique characteristics of intuitionistic fuzzy metrics. We aim to bridge the gap between traditional convergence concepts and their statistical counterparts by establishing a framework for analyzing sequence convergence under this new definition. Our exploration examines the relationships between various types of convergence, including the effects of scalar multiplication and sequence addition, while addressing the uniqueness of limits in the context of sliding window statistical convergence and the conditions governing these relationships.</p>

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On \(\mu\)-sliding window statistical convergence of generalized fractional difference sequences in intuitionistic fuzzy normed spaces

  • SK Ashadul Rahaman,
  • M. Mursaleen,
  • T. Tanushri

摘要

In this paper, we focus on the notion of sliding window statistical convergence of generalized fractional difference sequences by introducing the \(\Delta^{a,b,c}_{_{\varrho, \vartheta}}(\mu)\) Δ ϱ , ϑ a , b , c ( μ ) -convergence, which extends classical notions of convergence of fractional difference sequences to accommodate the unique characteristics of intuitionistic fuzzy metrics. We aim to bridge the gap between traditional convergence concepts and their statistical counterparts by establishing a framework for analyzing sequence convergence under this new definition. Our exploration examines the relationships between various types of convergence, including the effects of scalar multiplication and sequence addition, while addressing the uniqueness of limits in the context of sliding window statistical convergence and the conditions governing these relationships.