Orhan, HalitMurugusundaramoorthy, GangadharanCaglar, Murat2026-03-262026-03-2620220352-96652406-047X10.22190/FUMI201022034Ohttps://doi.org/10.22190/FUMI201022034Ohttps://hdl.handle.net/20.500.14901/2051Murugusundaramoorthy, Gangadharan/0000-0001-8285-6619The purpose of this article is to introduce a new subclass of analytic and bi-univalent functions, in associated with sigmoid function and to investigate the upper bounds for |a(2)| and |a(3)|, where a(2), a(3) are the initial Taylor-Maclaurin coefficients. Further, we obtain the Fekete-Szego 5 inequalities for this subclass of the bi-univalent function class sigma. We also give several illustrative examples of the bi-univalent function class which we introduce here.eninfo:eu-repo/semantics/openAccessAnalytic FunctionsUnivalent FunctionsBi-Univalent FunctionsSigmoid FunctionUpper BoundsFekete-Szego ProblemSubordination Between Analytic FunctionsArticle