Generalized Dual $s$-Frames and Their Perturbations in $S$-Hilbert Spaces
Received:August 28, 2025  Revised:February 25, 2026
Key Words: soft Hilbert space   dual soft frame   generalized dual   perturbation  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12461016) and the Natural Science Foundation of Henan Province (Grant Nos.252300420353; 252300421973; 252300421974; 262300421892).
Author NameAffiliation
Fu Yanling School of Statistics and Mathematics, Henan Finance University, Zhengzhou, Henan 450046, P. R. China 
Bai Xiaobei School of Statistics and Mathematics, Henan Finance University, Zhengzhou, Henan 450046, P. R. China 
Tian Yu School of Mathematics and Information Sciences, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, P. R. China 
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DOI:10.3770/j.issn:2095-2651.2026.04.008
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