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In this paper we introduce and investigate two new subclasses HΣq (α, λ) and HΣq(β, λ) of analytic and bi-univalent functions in the open unit disk U . Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3| for functions in these new subclasses. [ABSTRACT FROM AUTHOR]

In our present investigation, we first introduce several new subclasses of analytic and bi-univalent functions by using a certain q-integral operator in the open unit disk U = {z : z ∊ Cand z < 1}. By applying the Faber polynomial expansion method as well as the q-analysis, we then determine bounds for the nth coefficient in the Taylor-Maclaurin series expansion for functions in each of these newly-defined analytic and bi-univalent function classes subject to a gap series condition. We also highlight some known consequences of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce certain new subclasses of bi-univalent functions in open unit disk associated with the Srivastava-Attiya operator. We obtain coeffcient bounds |α2| and |α3| for the functions belonging to these new classes. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences of our main results, which are pointed out herein. [ABSTRACT FROM AUTHOR]

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U. In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results. [ABSTRACT FROM AUTHOR]

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this paper, we first investigate the relationship between various known classes of q-starlike functions that are associated with the Janowski functions. We then introduce and study a new subclass of q-starlike functions that involves the Janowski functions. We also derive several properties of such families of q-starlike functions with negative coefficients including (for example) distortion theorems. [ABSTRACT FROM AUTHOR]