In this work some distortion theorems and relations between the coefficients of normalized univalent harmonic mappings from the unit disc onto domains on the direction of imaginary axis are obtained.

The class of univalent harmonic functions on the unit disc satisfying the condition ∑∞ k=2 (k m − αk)(|ak|+ |bk|) ≤ (1−α)(1−|b1|) is given. Sharp coefficient relations and distortion theorems are given for these functions. In this paper we find that many results of Özturk and Yalcin [5] are incorrect. Some of the results of this paper correct the theorems and examples of [5]. Further, sharp coe...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

Abstract. The author here wish to further study the new concept of analytic and univalent functions normalized with f(ω) and f ′(ω) − 1 = 0 introduced by Kanas and Ronning in 1999 which was later also investigated in 2005 by Acu and Owa. The author in this paper obtain coefficient estimates, distortion theorems, convex linear combinations, and radii of ω-closeto-convex, ω − starlikeness and ω −...

The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also pr...

We will give the relation between the class of Janowski starlike functions of complex order and the class of Janowski convex functions of complex order. As a corollary of this relation, we obtain the radius of starlikeness for the class of Janowski convex functions of complex order. 1. Introduction. Let F be the class of analytic functions in D = {z | |z| < 1}, and let S denote those functions ...

Sanford S. Miller and Petru T. Mocanu’s theory of second-order differential subordinations was extended for the case third-order by José A. Antonino in 2011. In this paper, new results are proved regarding that extend ones involving classical subordination theory. A method finding a dominant is provided when behavior function not known on boundary unit disc. Additionally, obtaining best present...

In Geometric function theory, occasionally, attempts have been made to solve a particular problem for the Ma-Minda classes, $$\mathcal {S}^*(\psi )$$ and {C}(\psi of univalent starlike convex functions, respectively. Recently, popular radius generally known as Bohr’s phenomenon has studied in various settings; however, little is about Rogosinski radius. this article, fixed $$f\in \mathcal or ),...

In this paper we obtain upper bounds for the second Hankel determinant H2(2) of the classes bi-starlike and bi-convex functions of order β, which we denote by S∗ σ(β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinat H2(2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.

The purpose of the present paper is to study a certain subclass of harmonic univalent functions associated with Dziok-Srivastava operator. We obtain coefficient conditions, distortion bounds, and extreme points for the above class of harmonic univalent functions belonging to this class and discuss a class preserving integral operator. We also show that class studied in this paper is closed unde...