Certain Multiple Valued Harmonic Function

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

Blanket Algebra for Multiple-valued Function Decomposition

We consider functions of the form f : are only partially speciied. In general, f assigns to any output y i a nonempty set d 2 D of elements of E. If d = feg for some e 2 E, then y i has the value e. If d = E, then y i is a \complete don't care", i.e., is allowed to take on any value in E. In other cases, y i is a \limited don't care", allowed to take on any value in d. Moreover, the functions a...

Certain Convex Harmonic Functions

On certain subclasses of univalent $p$-harmonic mappings

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...

A certain convolution approach for subclasses of univalent harmonic functions

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.