Harmonic close-to-convex mappings associated with Salagean \(q\)-differential operator
DOI:
https://doi.org/10.24193/subbmath.2025.1.03Keywords:
Salagean q-differential operator, analytic functions, harmonic functions, partial sumsAbstract
In this paper, we define a new subclass \(\mathcal{W}(n,\alpha ,q)\) of analytic functions and a new subclass \(\mathcal{W}_\mathcal{H}^{0}(n,\alpha ,q)\) of harmonic functions \(f=h+\overline{g}\in \mathcal{H}^{0}\) associated with Salagean \(q\)-differential operator. We prove that a harmonic function \(f=h+\bar{g}\) belongs to the class \(\mathcal{W}_\mathcal{H}^{0}(n,\alpha ,q)\) if and only if the analytic functions \(h+\epsilon g\) belong to \(\mathcal{W}(n,\alpha ,q)\) for each \(\epsilon \ (|\epsilon| = 1)\), and using a method by Clunie and Sheil-Small, we determine a sufficient condition for the class \(\mathcal{W}_\mathcal{H}^{0}(n,\alpha ,q)\) to be close-to-convex. We provide sharp coefficient estimates, sufficient coefficient condition, and convolution properties for such functions classes. We also determine several conditions of partial sums of \(f\in\mathcal{W}_\mathcal{H}^{0}(n,\alpha ,q)\).References
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