Planar harmonic functions are complex-valued functions whose real and imaginary parts are
not necessarily conjugate, ie, do not need to satisfy the Cauchy-Riemann equations …

The primary objective of this paper is to explore the application of a specific convolution
operator, which incorporates the Pascal distribution series. Through this investigation, we …

The purpose of this paper is to find new inclusion relations of the harmonic class HF (ϱ, γ)
with the subclasses S HF*, K HF and TN HF (τ) of harmonic functions by applying the …

Many authors have obtained some inclusion properties of certain subclasses of univalent
and functions associated with distribution series, such as Pascal distribution, Binomial …

Let X= Spec (A) be a smooth affine variety of dimension n≥ 2 over a field k and P be a
projective A-module of rank n. A result of Murthy ([Mu], Theorem 3.8) says that if k is an …

In Section 1, we recall some basic facts about planar harmonic mappings. In Section 2, we
present harmonic analog of the classical Schwarz'lemma and its applications. In Section 3 …

In this paper, we introduce and study a subclass of harmonic univalent functions defined by
convolution and integral convolution. Coefficient bounds, extreme points, distortion bounds …

Let ϕ (z) be a fixed harmonic functions of the form φ(z)=z+∑k=2^∞c_kz^k+∑k=1^∞d_kz^k
(dk≥ ck≥ c 2> 0; k≥ 2) and SH (ck, dk, δ) be the subclass of harmonic univalent functions f …

The purpose of the present paper is to establish some interesting results involving coefficient
conditions, extreme points, distortion bounds and covering theorems for the classes $ V_H …

The purpose of the present paper is to establish some results involving coefficient
conditions, distortion bounds, extreme points, convolution, convex combinations and …