Scholarlink

<p>In this paper, we propose a new mathematical framework termed the <i>q</i>-<i>f</i>-divergence, constructed using the <i>q</i>-integral operator from quantum calculus. This novel divergence measure extends traditional notions of divergence by embedding them within a <i>q</i>-calculus setting, which allows for greater flexibility in handling non-classical or parameterized probability distributions. Our formulation generalizes key ideas originally presented in&#xa0;Lin (<CitationRef CitationID="CR27">1991</CitationRef> IEEE Trans Inf Th 37(1), 145–151), particularly by recovering classical results in the limiting case where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q \rightarrow 1\)</EquationSource> </InlineEquation>. We rigorously examine the structural properties of the <i>q</i>-<i>f</i>-divergence, including its behavior under convex transformations and its alignment with information-theoretic criteria. The generalized framework opens the door to deeper theoretical insights and may support more refined tools for applications in statistical inference, coding theory, and information geometry. Our results demonstrate the strength and potential versatility of the <i>q</i>-<i>f</i>-divergence in both classical and quantum contexts.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the f-divergence on Quantum Calculus

  • 期刊论文

  • 发表日期：

    2025年11月18日

查看全文
  • Saeed Kosari,
  • Milad Yadollahzadeh,
  • MohammadHossein Derakhshan,
  • Seyed Abdollah Beikaee

摘要

In this paper, we propose a new mathematical framework termed the q-f-divergence, constructed using the q-integral operator from quantum calculus. This novel divergence measure extends traditional notions of divergence by embedding them within a q-calculus setting, which allows for greater flexibility in handling non-classical or parameterized probability distributions. Our formulation generalizes key ideas originally presented in Lin (1991 IEEE Trans Inf Th 37(1), 145–151), particularly by recovering classical results in the limiting case where \(q \rightarrow 1\) . We rigorously examine the structural properties of the q-f-divergence, including its behavior under convex transformations and its alignment with information-theoretic criteria. The generalized framework opens the door to deeper theoretical insights and may support more refined tools for applications in statistical inference, coding theory, and information geometry. Our results demonstrate the strength and potential versatility of the q-f-divergence in both classical and quantum contexts.