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Three new subfamilies of multivalent (or p -valent) q-starlike functions with respect to higher-order q-derivatives are introduced. Several properties of such families of qstarlike functions with negative coefficients including distortion theorems and radius problems are derived. For the motivation and validity of the results which are presented here, relevant connections of our findings with those that were given in earlier work are also pointed out. Finally, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward ), ( q p -variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter p is obviously redundant. [ABSTRACT FROM AUTHOR]

A new class of q-close-to-convex functions associated with Janowski functions is defined. In this regard, we give sufficient conditions and prove famous de Branges theorem for this newly-defined class of q-close-to-convex functions. We also give the application of our results to finding sufficient conditions for the celebrated Mittag-Leffler function to be a Janowski q-close-to-convex function. [ABSTRACT FROM AUTHOR]

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 this paper we introduce certain new subclasses of multivalent spiral-like functions by means of the concept of k-uniformly star-likness and k-uniformly convexity. We prove the inclusion relations, sufficient condition and Fekete-Szegö inequality for these classes of functions. The behaviour of these classes under a certain integral operator is also discussed. [ABSTRACT FROM AUTHOR]

In this paper we introduce and study a new subclass Rp of p-valent functions that are analytic in the open unit disk E = {z: ∣ z ∣< 1}. Some interesting results by using convolution technique for this subclass Rp are obtained. Also, we point out some known consequences of our main results. [ABSTRACT FROM AUTHOR]