New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials

Coefficient Estimates for a New Subclasses of m-fold Symmetric Bi-Univalent Functions

The purpose of the present paper is to introduce two new subclasses of the function class ∑m  of bi-univalent functions which both f  and f-1  are m-fold symmetric analytic functions. Furthermore, we obtain estimates on the initial coefficients for functions in each of these new subclasses. Also we explain the relation between our results with earlier known results.

Some new subclasses of bi-univalent functions

The purpose of the present paper is to obtain the initial coefficients for normalized analytic functions f in the open unit disk U with its inverse g = f−1 belonging to the classes H σ (φ), ST n σ (α, φ), M n σ (α, φ) and L n σ(α, φ). Relevant connections of the results presented here with various known results are briefly indicated. Finally, we give an open problem for the readers. Mathematics...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Some Results for Univalent Functions Defined with Respect to N-symmetric Points

The criteria that embed a normalized analytic function in the class of functions that are starlike with respect to N-symmetric points are presented. The criteria are based on the quotient of analytical representations of starlikeness and convexity with respect to N -symmetric points. AMS Mathematics Subject Classification (2000): 30C45

Coefficient Estimates for New Subclasses of Meromorphic Bi-Univalent Functions

We introduce and investigate two new subclasses ℳ σ (α, λ) and ℳ σ (β, λ) of meromorphic bi-univalent functions defined on Δ = {z : z ∈ ℂ, 1 < |z | <∞}. For functions belonging to these classes, estimates on the initial coefficients are obtained.