On the f-divergence on Quantum Calculus

Saeed Kosari, Milad Yadollahzadeh (), MohammadHossein Derakhshan and Seyed Abdollah Beikaee
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Saeed Kosari: Guangzhou University
Milad Yadollahzadeh: Babol Noshirvani University of Technology
MohammadHossein Derakhshan: Apadana Institute of Higher Education
Seyed Abdollah Beikaee: Qom University of Technology

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-13

Abstract: Abstract 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.

Keywords: q-integral operators; q-special functions; f-divergence; qHH-f-divergence; 05A30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10222-1

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