The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly ...

In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized with f (w) = f ′(w)− 1 = 0 and w a fixed point in U . In 2005, the authors introduced the classes of functions close to convex and α-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that ...

Let HC ( ? ) and c denote the classes of sense-preserving harmonic mappings f = h + g ¯ in D with dilation ? z ? for | < 1 such that is Ma–Minda type convex function respect to conjugate points respectively. Here, : ? ? , called function, analytic univalent has positive real part, symmetric axis, starlike 0 > . The are derived from work Sun et al. (2016) on class M ? We study growth theorems fu...

In this paper, we mainly consider the convolutions of slanted half-plane mappings and strip unit disk D. If f1 is a mapping f2 or mapping, then prove that * convex in some direction if locally univalent We also obtain two sufficient conditions for to be Our results extend many recent direction. Moreover, class harmonic including mappings, as consequence, any combination such sense-preserving co...

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

In this paper, we generalize and investigate the Bohr-Rogosinski inequalities property for subfamilies of univalent functions defined on unit disk D:={z∈C:|z|<1} which maps to concave domain, i.e., domain whose complement is a convex set. All results are proved be sharp.

We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....