Univalent functions, fractional calculus, and their applications , edited by H. M. Srivastava and S. Owa. Pp 404. £39·95. 1989. ISBN 0-7458-0701-1 (Ellis Horwood)

Coefficient estimates for a subclass of analytic and bi-univalent functions

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$ . By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

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Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions

In the present paper, we obtain the upper bounds for the second Hankel determinant for certain subclasses of analytic and bi-univalent functions. Moreover, several interesting applications of the results presented here are also discussed.

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Second Hankel determinant for certain subclasses ofbi-univalent functions

In this paper, the concepts of Janowski functions and the conic regions are combined to define a new domain which represents the conic type regions. Different views of this modified conic domain for specific values are shown graphically for better understanding of the behavior of this domain. The class of such functions which map the open unit disk E onto this modified conic domain is defined. Also the classes of k-uniformly Janowski convex and k-Janowski starlike functions are defined and their coefficient inequalities are formulated. The coefficient bound for a certain class of analytic functions, proved by Owa et al. (2006) in [16], has also been improved.

On coefficient inequalities of functions associated with conic domains

In this paper, we introduce and investigate each of the following subclasses: SΣ(λ,γ;ϕ), HS Σ(α), RΣ(η,γ;ϕ) and BΣ(μ;ϕ) (0 λ 1; γ ∈ C� {0}; α ∈ C ;0 η 0, and ϕ(D) is symmetric with respect to the real axis. We obtain coefficient bounds involving the Taylor-Maclaurin coefficients |a2| and |a3| of the function f when f is in these classes. The various results, which are presented in this paper, would generalize and improve those in related works of several earlier authors.

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Certain subclasses of bi-univalent functions satisfying subordinate conditions

Second Hankel determinant for bi-starlike and bi-convex functions of order β

By using a linear multiplier fractional differential operator a new subclass of analytic functions generalized @b-uniformly convex functions, denoted by @b-SP"@l","@m^n^,^@a(@c), is introduced. For this class the Fekete-Szego problem is completely solved. Various known or new special cases of our results are also pointed out.

The Fekete-Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains

In this paper the method of subordination chains is used to establish some su‐cient conditions for univalence for analytic functions deflned in the open unit disk.

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Erhan Deniz

Papers

Certain subclasses of bi-univalent functions satisfying subordinate conditions

Second Hankel determinant for certain subclasses ofbi-univalent functions

Second Hankel determinant for bi-starlike and bi-convex functions of order β

The Fekete-Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains

On some sufficient conditions for univalence