Let Σp denote the class of functions normalized by f(z) = z−p + ∞ ∑ n=1 anz n−p (p ∈ N), which are analytic and p-valent in 0 < |z| < 1. Making use of a linear operator, which is defined here by the generalized hypergeometric function, we introduce some new subclasses of the meromorphically p-valent function class Σp and investigate their inclusion relationships. Mathematics Subject Classificat...

In the present paper, we develop some implications leading to Carathéodory functions in open disk and provide new conditions for be p-valent functions. This work also extends findings of Nunokawa others.

In a recent paper [2], G. R. Blakley raised a question about the decomposition of a ^-valent starlike function into the product of two ^-valent starlike functions. It is the purpose of this note to prove the conjecture of Blakley. Definition 1. The function/(z), regular in |z| <1, is said to be in the class S(p, m), where p and m are positive integers with p^m, if and only if (1) there exists a...

in this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎some of our results improve‎ ‎and generalize previously known results‎.

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass analytic and multivalent p-valent) functions class Ap, where Ap is invariant symmetric) under rotations. The well-known Janowski are used with help principle subordination between in order to p-valent functions. This function generalizes various other subclasses functions, not only classical Geometric...

In this paper we introduce the class B(p, n, μ, α) of analytic and p-valent functions to obtain some sufficient conditions and some angular properties for functions belonging to this class.

The idea of fuzzy differential subordination is a generalisation the traditional that evolved in recent years as result incorporating set into field geometric function theory. In this investigation, we define some general classes p-valent analytic functions defined by and generalizes various classical results multivalent functions. Our main focus to discuss interesting inclusion other useful pr...