which are analytic in the open unit disk U {z ∈ C : |z| < 1}. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z if there exists an analytic function w in U with w 0 0 and |w z | < 1 for z ∈ U such that f z g w z . We denote by S∗, K, and C the subclasses of A consisting of all analytic functions which are, respectively, starlike, convex, and close-to-co...

The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all a...

In the present paper, we introduce new subclasses of bi-starlike and bi-convex functions complex order associated with Erdély–Kober-type integral operator in open unit disc find estimates initial coefficients these classes. Moreover, obtain Fekete-Szegő inequalities for Some significances our results are pointed out as corollaries.

Keywords: Analytic functions Starlike and convex functions Multivalent functions Hadamard product (or convolution) Coefficient bounds Distortion inequalities Neighborhood properties Non-homogeneous Cauchy–Euler differential equations a b s t r a c t In this paper, by making use of the familiar concept of neighborhoods of p-valently analytic functions, we prove coefficient bounds, distortion ine...

The logarithmic coefficients are very essential in the problems of univalent functions theory. importance is due to fact that bounds on f can transfer Taylor themselves or their powers, via Lebedev–Milin inequalities; therefore, it interesting investigate Hankel determinant whose entries coefficients. main purpose this paper obtain sharp for second strongly starlike and convex functions.

"Let $C$ and $S^*$ stand for the classes of convex starlike mapping in $\D$, let $\cc$, $\cs$ denote closures respective hulls. We derive characterizations when convolution mappings $\cc$ is convex, as well starlike. Several terms are given convexity within starlikeness $\cs$. also obtain a correspondence via between $S^*$, correspondences subclasses that have $n$-fold symmetry."

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution open unit disk U. Using Hadamard product or convolution, function fs(z) is defined as involving an and expressed terms of functions. Neighborhood properties for are established. Further, by applying a previously introduced linear transformation using extended Libera in...

It is well known [28] that a number of important classes of univalent functions (e.g. convex, starlike) are related through their derivatives by functions with positive real part. These functions play an important part in problem from signal theory, in moment problems and in constructing quadrature formulas, see Ronning [97] and the references cited therein for some recent applications. In this...

We introduce two subclasses T ∗(p, α, j) and C(p, α, j) (0 ≤ α < p − j + 1, 1 ≤ j ≤ p, p ∈ N = {1, 2, . . .}) of p-valent starlike and p-valent convex functions with negative coefficents. In this paper we obtain coefficient inequalities, distortion theorems, extreme points and integral operators for functions belonging to the classes T ∗(p, α, j) and C(p, α, j). We also determine the radii of c...

We are interested in finding the sufficient conditions on A , B , λ , b and c which ensure that the generalized Bessel functions uλ := uλ ,b,c satisfies the subordination uλ (z) ≺ (1+Az)/(1+Bz) . Also, conditions for which uλ (z) to be Janowski convex, and zuλ (z) to be Janowski starlike in the unit disk D = {z ∈ C : |z| < 1} are obtained. Mathematics subject classification (2010): 34B30, 33C10...