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Keywords = Jung–Kim–Srivastava operator

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Article
Janowski-Type q-Classes Involving Higher-Order q-Derivatives and Fractional Integral Operators
by Loriana Andrei and Vasile-Aurel Caus
Fractal Fract. 2025, 9(11), 699; https://doi.org/10.3390/fractalfract9110699 - 30 Oct 2025
Abstract
In this paper, we address the lack of general Janowski-type subclasses for analytic functions involving higher-order q-derivatives, unifying cases with both positive and negative coefficients. Using a combination of higher-order q-derivative techniques and Janowski subordination, we introduce two new q-analytic [...] Read more.
In this paper, we address the lack of general Janowski-type subclasses for analytic functions involving higher-order q-derivatives, unifying cases with both positive and negative coefficients. Using a combination of higher-order q-derivative techniques and Janowski subordination, we introduce two new q-analytic classes and derive sharp coefficient inequalities that fully characterize them. Our main theorems provide explicit coefficient bounds, distortion and neighborhood inclusion results, extending the classical Goodman–Ruscheweyh theory to the q-calculus setting. Applications are given to fractional q-integral operators, in particular to the q-Jung–Kim–Srivastava operator, and the results reduce to several known cases as q1. Full article
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