Citation :

Ooi Kuan Zack, Aini Janteng, Tseu Suet Yie, "Coefficient Estimates of New Subclasses of Analytic Functions of Complex Order," International Journal of Engineering Trends and Technology (IJETT), vol. 74, no. 1, pp. 152-159, 2026. Crossref, https://doi.org/10.14445/22315381/IJETT-V74I1P112

Abstract

The exploration of geometric characteristics and mapping of complex analytic functions has been actively developed since the late 19th century, leading to the field known as geometric function theory. One of the well-known problems in geometric function theory is the Fekete-Szegö problem, which seeks to determine the best possible bounds for certain functionals involving the differences of coefficients in the Taylor series expansion of analytic functions. This study aims to introduce new subclasses of analytic functions, ℳ𝑞,𝜆(𝜓) and ℒ𝑞,𝜆(𝜓), which are defined using the Sălăgeăn q-differential operator. This study also establishes the upper bounds on the Fekete-Szegö functional |𝒶3 − 𝜂𝒶2 2| for functions in the new subclasses.

Keywords

Analytic functions, Fekete-Szegö functional, Geometric function theory, Quantum (or q-) calculus, q-Differential operator.

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