MMN-5063
Study on a subclass of holomorphic functions associated to the q-analogue multiplier transformation defined in a Janowski domain
Ibtisam Aldawish; Abbas Kareem Wanas; Georgia Irina Oros; Sheza M. El-Deeb;Abstract
The present study uses differential subordination in conjunction with Janowski type functions to establish the particular class F(m,n,λ,q,D,E) of holomorphic functions in the open unit disk. This class is associated with the q-analogue multiplier transformation. Using both the Keogh-Merkes and Ma Minda’s inequalities and the well-known Carathéodory’s inequality for functions with positive real parts, an upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion is derived. Also, for the functions in this family, an upper bound on the Fekete-Szegö functional is provided. Furthermore, for the function G−1, a similar conclusion is derived for the Fekete-Szegö inequality and the first two coefficients when G ∈ F(m,n,λ,q,D,E). Properties regarding partial sums, necessary and sufficient conditions for functions to be part of F(m,n,λ,q,D,E), radii of close-to-convexity and starlikeness for this class, as well as distortion bounds are also established. The novelty of the results consists in the investigation of the basic properties of the new class of functions using simple methods, and the fact that the class is connected with the new above mentioned q-operator and the Janowski functions.
Vol. 27 (2026), No. 1, pp. 15-33