Some Sharp Neighborhoods of Univalent Functions

Some Sharp Neighborhoods of Univalent Functions

For 5 > 0 and /(z) = z + a2z2 + ••■ analytic in \z\ < 1 let the 5neighborhood of/, Ns(f), consist of those analytic functions g(z) — z + b2z2 + ••• with E"_2 k\ak bk\ < S. We determine sufficient conditions guaranteeing which neighborhoods of certain classes of convex functions belong to certain classes of starlike functions. We extend some recent results of St. Ruscheweyh and R. Fournier and, ...

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 Generalized Convolution of Harmonic Univalent Functions

The purpose of the present paper is to investigate some interesting properties on generalized convolutions of functions for the classes HP ∗(α),HS(α) andHC(α). Further, an application of the convolution on certain integral operator are mentioned. AMS 2010 Mathematics Subject Classification : 30C45, 26D15.

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.

Univalent Functions with Univalent Derivatives. Ii