Harmonic close-to-convex mappings associated with Sălăgean q-differential operator - MISHRA, Omendra; ÇETINKAYA, Asena; SOKÓŁ, Janusz (Studia Universitatis Babeș-Bolyai Mathematica, 2025)
In this paper, we define a new subclass W(n, α, q) of analytic functions and a new subclass WH0 (n, α, q) of harmonic functions f = h+g¯ ∈ H0 associated with Sălăgean q-differential operator. We prove that a harmonic function f = h+g¯ belongs to the class WH0 (n, α, q) if and only if the analytic functions h+ϵg belong to W(n, α, q) for each ϵ (|ϵ| = 1), and using a method by Clunie and Sheil-Small, we determine a sufficient condition for the class WH0 (n, α, 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∈ WH0 (n, α, q). Mathematics Subject Classification (2010): 31A05, 30C45, 30C55. Received 05 November 2023; Accepted 28 December 2024.