Geometric Properties of Janowski-type Harmonic Functions Involving Bessel Functions
Abstract
In this paper, we characterize geometric properties and inclusion relationships of particular subclasses of harmonic univalent functions in U = {ξ ∈ C : |ξ| < 1}. By employing a convolution operator constructed via Bessel functions of generalized type, we establish new relationships between Janowski-type harmonic starlike functions and several well-known harmonic subclasses, including harmonic convex, starlike, close to-convex, and Ruscheweyh-type classes. Sufficient coefficient criterias are derived to guarantee that the introduced operator preserves membership in the Janowski-type harmonic class S∗ H(E,W). Furthermore, we obtain some inclusion conclusions. The obtained criteria are expressed in terms of the values and derivatives of the associated generalized Bessel functions at unity. Our conclusions extend and refine several earlier works in the literature concerning harmonic mappings associated with special functions. In particular, they
provide a unified framework for studying Janowski-type harmonic functions involving generalized Bessel functions and open the way for further investigations via other special function operators.
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