Given the hypergeometric function F (a, b; c; z) = ∞ P n=0 (a)n(b)n (c)n(1)n zn, we place conditions on a, b and c to guarante that zpF (a, b; c; z) will be in various subclasses of p-valent starlike and p-valent convex functions. Operators related to the hypergeometric function are also examined.

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

The objective of this paper is to obtain an upper bound to the second Hankel determinant |ap+1ap+3 − ap+2| for p-valent starlike and convex functions of order α, using Toeplitz determinants. AMS Mathematics Subject Classification (2010): 30C45, 30C50

Making use of Srivastava-Wright operator we introduced a new class of complexvalued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, convex combination. Mathematics subject classification (2010): 30C45.

Abstract For functions f(z) which are starlike of complex order b (b = 0) in the open unit disk U introduced by M. A. Nasr and M. K. Aouf (J. Natural Sci. Math. 25(1985), 1 12), in consideration of its properties, some sufficient conditions, necessary conditions and distortion theorems with coefficient inequalities of f(z) as the improvement of the well-known result due to H. Silverman (Proc. A...

Commons Attribution-Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 15 Issue 10 Version 1.0 Year 2015 Type : Double Blind Peer Reviewed Internatio...

Let f be a normalized analytic function defined on the unit disk and fλ z : 1 − λ z λf z for 0 < λ ≤ 1. For α > 0, a function f ∈ SP α, λ if zf ′ z /fλ z lies in the parabolic region Ω : {w : |w − α| < Rew α}. Let CP α, λ be the corresponding class consisting of functions f such that zf ′ z ′/f ′ λ z lies in the region Ω. For an appropriate δ > 0, the δ-neighbourhood of a function f ∈ CP α, λ i...

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, discuss geometric properties classes, such as integral expression, coefficient estimation, distortion theorem, Jacobian growth estimates, and covering theorem.