In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto whole complex plane. We also establish connection between boundary functions harmonic and biharmonic mappings. Finally, show how close-to-convex can be constructed from convex mapping.

A complex valued function f = u+ iv defined in a domain D ⊂ C, is harmonic in D, if u and v are real harmonic. Such functions can be represented as f(z) = h(z) + g(z), where h an g are analytic in D. In this paper we study some convolution properties preserved by the integral operator In H,λf, n ∈ N0 = N ∪ {0}, λ > 0, where the functions f are univalent harmonic and sense-preserving in the open...

Many authors have obtained some inclusion properties of certain subclasses univalent and functions associated with distribution series, such as Pascal distribution, Binomial Poisson Mittag–Leffler-type Geometric distribution. In the present paper, we obtain relations harmonic class H(α,δ) classes SH* starlike KH convex functions, also for TNHβ TRHβ operator Υ defined by applying convolution reg...

The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results which are associated with certain clas...