A class of expanded analytic functions and Fekete-Szeg problem

Using the definition of subordination,a new class A(λ,α,σ,β) function is introduced modeling on the definition of B(λ,α,σ,β).Using Tuneski's research and some methods in complex analysis,the inclusion relation B(λ,α,σ,β)A(λ,α,σ,β) in the interval |z|r1=2～(1/2)-1 is obtained.Using the properties of subordination of Liu Mingsheng's research,the Fekete-Szeg inqualities for A(λ,α,σ,β) are discussed.By some calculations the Fekete-Szeg inqualities in μ≤μ1,μ1≤μ≤μ2 and μ2≤μ≤μ3 are obtained.Further,the sharp function in μ2≤μ≤μ3 is obtained which generalize the related results of some authors.