Some conditions for the Touchard polynomials to be in subclasses of analytic functions
Wafaa Y. Kota, Rabha M. El-Ashwah
Received January 5, 2025. Published online September 1, 2025.
Abstract: This paper discusses certain criteria that must be satisfied for a Touchard polynomial to belong to subclasses of analytic functions. Also, we obtain some inclusion relations between the classes $\mathfrak{U}_{\sigma}(D,E)$ and $\widehat{\mathcal{M}}(\eta,\mu)$. We also go over the geometric characteristics of an integral operator that has to do with the Touchard polynomial. Some particular instances of our primary discoveries are also remarked upon and discussed.
Keywords: Touchard polynomial; analytic function; integral operator; Hadamard product; univalent function
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Affiliations: Wafaa Y. Kota (corresponding author), Rabha M. El-Ashwah, Department of Mathematics, Faculty of Science, Damietta University, 34511 New Damietta, Egypt, e-mail: wafaa_kota@yahoo.com, r_elashwah@yahoo.com
