New criteria for univalent functions

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

Differential Inequalities and Criteria for Starlike and Univalent Functions

The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f satisfying the condition ∣∣∣1 + zf ′′(z) 2f ′(z) − zf ′(z) f(z) ∣∣∣ < β, z ∈ Δ implies that f is univalent or ...

Estimates for Univalent Functions

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...

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.