On Harmonic Functions Defined by Differential Operator with Respect tok-Symmetric Points

On Meromorphic Harmonic Functions with Respect to k-Symmetric Points

Bi-concave Functions Defined by Al-Oboudi Differential Operator

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

On Harmonic Functions Defined by Derivative Operator

A sufficient coefficient of this class is determined. It is shown that this coefficient bound is also necessary for the classM –– H n, λ, α if fn z h –– gn∈ MH n, λ, α , where h z z− ∑∞ k 2|ak|z, gn z −1 n ∑∞ k 1|bk|z and n ∈ N0. Coefficient conditions, such as distortion bounds, convolution conditions, convex combination, extreme points, and neighborhood for the class M –– H n, λ, α , are obta...

On a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator

In this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎Some of our results improve‎ ‎and generalize previously known results‎.

on a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator

in this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎some of our results improve‎ ‎and generalize previously known results‎.