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.
In the present work, we propose to investigate the Fekete-Szego inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerni
ng different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.
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.
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.
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, neighbor
hoods and partial sums for functions f(z) belonging to this class.
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.
In the present paper the new multiplier transformations $mathrm{{mathcal{J}% }}_{p}^{delta }(lambda ,mu ,l)$ $(delta ,lgeq 0,;lambda geq mu geq 0;;pin mathrm{% }%mathbb{N} )}$ of multivalent functions is defined. Making use of the operator $mathrm{%
{mathcal{J}}}_{p}^{delta }(lambda ,mu ,l),$ two new subclasses $mathcal{% P}_{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$ and $widetilde{mathcal{P}}% _{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$textbf{ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $mathcal{P}_{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$ and $widetilde{mathcal{P}}_{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.
In this paper we introduce and study two new subclasses Sigma_{lambdamu mp}(alpha,beta)$ and $Sigma^{+}_{lambdamu mp}(alpha,beta)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connec
ted to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.
