A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

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.

Let SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ∞ ∑ n=2 anz , g(z) = ∞ ∑

"In this paper, two subclasses of biholomorphic starlike mappings named Janowski and almost with complex parameters are introduced studied. We determine $M$ such that holomorphic $f$ which satisfy the condition $\|Df(z)-I\|\le M$, $z\in B^n$, starlike, respectively starlike. also derive sufficient conditions for normalized (expressed in terms their coefficient bounds) to belong one mentioned ab...

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f satisfying the conditions that zf (z)/f(z) and zg(z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known ...

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.