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Mathematical Methods in the Applied Sciences, vol.48, no.4, pp.1-12, 2025 (Scopus)
The motivation of this paper is to explore and generalize Sakaguchi-type functions, which play a significant role in geometric
function theory. In this context, we introduce four new classes of analytic univalent functions: ℑ𝑏,𝛼,𝜌
Ψ,𝑡
, ℑ𝑏,𝛼,𝜌
𝜗
, ℑ𝑏,𝛼,𝜌
Θ,𝑚 , and ℑ𝑏,𝛼,𝜌
Ξ,𝑘 .
These classes are defined to extend the study of these functions and their applications. First, we define the class ℑ𝑏,𝛼,𝜌
Ψ,𝑡 , associated
with generalized telephone numbers, using the concept of subordination. For functions 𝑢 in this class, we derive initial coefficient
estimates and address the Fekete–Szegö functional problem, as well as explore results for the inverse function 𝑢−1. Next, we
introduce the remaining classes ℑ𝑏,𝛼,𝜌
𝜗
, ℑ𝑏,𝛼,𝜌
Θ,𝑚 , and ℑ𝑏,𝛼,𝜌
Ξ,𝑘 which are connected to ℑ𝑏,𝛼,𝜌
Ψ,𝑡 through convolution and Borel and Poisson
distribution series. For these classes, we obtain variations of the Fekete–Szegö inequality and discuss their relationships with
previously studied function classes.