Second Hankel determinant for bi-starlike and bi-convex functions of order b{eta}

In the present investigation the authors obtain upper bounds for the second Hankel determinant of the classes bi-starlike and bi-convex functions of order beta.

Initial coefficient bounds for a general class of bi-univalent functions

Inspired by the recent works of Srivastava et al. (HMS-AKM-PG), Frasin and Aouf (BAF-MKA) and others (Ali-Ravi-Ma-Mina-class,Caglar-Orhan,Goyal-Goswami,Xu-HMS-AML,Xu-HMS-AMC), we propose to investigate the coefficient estimates for a general class of analytic and bi-univalent functions. Also, we obtain estimates on the coefficients |a2| and |a3| for functions in this new class. Some interesting remarks, corollaries and applications of the results presented here are also discussed.

Initial coefficient bounds for certain classes of Meromorphic bi-univalent functions

In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the coefficients |b0| and |b1| for functions in these new classes. Some interesting remarks and applications of the results presented here are also discussed.

Univalence Criteria and Quasiconformal Extensions

In the present paper, we obtain a more general conditions for univalence of analytic functions in the open unit disk U. Also, we obtain a refinement to a quasiconformal extension criterion of the main result.

Some generalizations on the univalence of an integral operator and quasiconformal extensions

By using the method of Loewner chains, we establish some sufficient conditions for the analyticity and univalency of functions defined by an integral operator. Also, we refine the result to a quasiconformal extension criterion with the help of Beckerss method.

On neighborhood and partial sums problem for generalized Sakaguchi type functions

In the present investigation, we introduce a new class k-US_{s}^{{eta}}({lambda},{mu},{gamma},t) of analytic functions in the open unit disc U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f(z) belonging to this class.

Some sufficient conditions for the univalence of an integral operator

Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a quasiconformal extension criterion of the main result, is also obtained.