Fekete-Szegö Problem for Certain Analytic Functions of Complex Order Associated With Cardioid Domain

In this present investigation, using a linear multiplier differential operator \(\mathfrak{D}{\mathfrak{\lambda,\mu }}^{\mathfrak{M}}f\left(\psi \right)\), we introduced a novel subclass of starlike and convex functions of complex order \(\gamma\) defined on the open unit disk \(\mathfrak{E}\), associated with cardioid domain. This subclass provides a solution to the Fekete-Szegö problem, along with the consideration of numerous new special cases.