In the present investigation, we obtain initial coefficients of λ− pseudo starlike functions related to sigmoid functions and the Fekete-Szegö coefficient functional |a 3 −µa 2 2 | for certain normalized analytic functions defined on the open unit disk. As an application of the main result,we pointed out the initial coefficients and Fekete-Szegö inequality for a subclasses of starlike functions related to sigmoid functions.

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We introduce and investigate a new subclass of the function class Σ of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients | 2 | and | 3 | for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.

We introduce a new class of meromorphic parabolic starlike functions with a fixed point defined in the punctured unit disk Δ * := { ∈ C : 0 < | | < 1} involving the -hypergeometric functions. We obtained coefficient inequalities, growth and distortion inequalities, and closure results for functions ∈ M ( , , ). We further established some results concerning convolution and the partial sums.

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out consequences of our main results.