Criteria of univalence and fully –accessibility forp–harmonic andp–analytic functions

Abstract

In this article, we present univalence criteria for polyharmonic and polyanalytic functions. Our approach yields new a criterion for a polyharmonic functions to be fully α-accessible. Several examples are presented to illustrate the use of these criteria.2000 Mathematics Subject Classification. Primary: 31A05, 31A30, 31C05, 30C45, 52A30; Secondary: 30C20.

Some coefficient estimates on real kernel 𝛼-harmonic mappings

“…If we take α = p − 1 is a nonnegative integer, then from Theorem 1.1 of [9], we find that the complexvalued kernel α−harmonic mapping is polyharmonic (exactly, p−harmonic). As to the general polyharmonic mappings, we refer to [1,2,6,7,14,23,24]. In particular, if α = 0, then the complex-valued kernel α−harmonic mapping is harmonic.…”

Lipschitz Continuity of Quasiconformal Mappings and of the Solutions to Second Order Elliptic PDE with Respect to the Distance Ratio Metric

“…[2,5,9,27]). Recently, several new properties of polyharmonic mappings are discussed in [2]. The following result concerns the solutions to the equation (1.3).…”

Dirichlet Problem, Univalency and Schwarz Lemma for Biharmonic Mappings

“…Investigation of biharmonic mappings in the context of geometric function theory is started only recently. Indeed several important properties of biharmonic mappings are obtained in [1,2,3,4,6,14,16] and these mappings were also generalized by some others, see for example [9,27] and the references therein. In the point of view of applied mathematics, biharmonic mappings arise naturally in fluid dynamics and elasticity problems, and have important applications in engineering and biology (see [22,25]).…”