The Fekete–Szegö Inequality for a Certain Subclass of Analytic Functions of Complex Order Related to the 𝔮-Srivastava–Attiya Operator

The use of integral and differential operators in geometric function theory has continued to gain interest among researchers in the field of study in recent times. This is due to the wide range of its applications in science, technology and engineering. In this work, therefore, the authors defined and investigated a new subclass of analytic functions in the open unit disk using the q-Srivastava–Attiya convolution operator and the Jackson’s q-derivative, by means of the subordination. The authors used two well-known lemmas to determine a sharp upper-bound for the Fekete–Szego¨ functional in two different cases. In particular, the authors introduced a new generalized subclass of complex order univalent functions denoted by Lq,b,hsτ,Φ and derived the coefficient estimates aι(ι=2,3) of the Taylor–Maclaurin series in this class, as well as the Fekete–Szego¨ inequality a3−ℵa22 for functions in this class. The work generalizes many known results in the literature.