Analysis of certain determinants for a defined subclass of analytic functions using Poisson distribution series in petal shaped domain - VIJAYALAKSHMI, Sangarambadi Padmanabhan; MEHDHA, Martin; PORWAL, Saurabh; EZHILARASI, Raman; SUDHARSAN, Thirumalai Vinjimur (Studia Universitatis Babeș-Bolyai Mathematica, 2026)
The current study focuses on obtaining the sharp coefficient estimates and Fekete-Szegö inequality for the class Ψϑ(m, λ) and uses the Poisson distribution series to obtain the sharp estimates of coefficient inequalities, Fekete-Szegö inequality, second order Toeplitz determinants and upper bounds of third order Toeplitz determinants and second order Hankel determinants for a certain analytic function U(z) = z + δ2z2 + δ3z3 + · · · , U(z) ̸= 0, z ∈ ∆ belonging to the class PΨϑ(m, λ, Υ) = U ∈ H : IkU ∈ Ψϑ(m, λ), m ∈ N0 = 0, 1, 2, · · · , λ, ϑ ∈ N = 1, 2, ..., Υ = Υi(k) = [ki−1/(i−1)!]e−k, defined on the open unit disc (z ∈ Δ := z : |z| < 1). This research could motivate others to delve deeper into the coefficient functional problem related to the Poisson distribution series of analytic functions across different categories of univalent functions. Mathematics Subject Classification (2010): 30C45, 30C50. Received 10 January 2026; Accepted 06 March 2026.