Harmonic beta-convex functions involving hypergeometric functions

Some integral inequalities for harmonic h-convex functions involving hypergeometric functions

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h-convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. In recent years, much attention have been given to theory of convexity beca...

Inclusion Theorems Involving Wright’s Generalized Hypergeometric Functions and Harmonic Univalent Functions

The purpose of this paper is to apply Wright generalized hypergeometric (Wgh) functions in defining a linear operator and obtain some inclusion relationships between the classes of harmonic univalent functions under this linear operator whenever certain Wgh inequalities with its validity conditions hold. Results for special cases of Wgh functions are also mentioned. 2000 Mathematics Subject Cla...

Certain Convex Harmonic Functions

Involvement of Hypergeometric Functions in The Theory of Harmonic Functions

Harmonic univalent mappings have attracted the serious attention of complex analysts only after the appearance of a basic paper by Clunie and Sheil-Small [4] in 1984. These researchers laid the foundation for the study of harmonic univalent mappings over the unit disk as a generalization of analytic univalent functions. Interestingly, almost at the same time, the famous Bieberbach conjecture wh...

On Harmonic Meromorphic Functions Associated with Basic Hypergeometric Functions

By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points.