Yong Sun

Bio: Yong Sun is an academic researcher from Hunan Institute of Engineering. The author has contributed to research in topics: Harmonic (mathematics) & Analytic function. The author has an hindex of 5, co-authored 12 publications receiving 63 citations. Previous affiliations of Yong Sun include Hunan University.

Linear combinations of harmonic quasiconformal mappings convex in one direction

Abstract: In this paper, we introduce a new class $\mathscr{S}_{H} (k, γ; \phi)$ of harmonic quasiconformal mappings, where $k \in [0,1), γ \in [0,π)$ and $\phi$ is an analytic function. Sufficient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of $γ$ and $\phi$, are convex.

Integral Representations and Coefficient Estimates for a Subclass of Meromorphic Starlike Functions

Abstract: In this paper, we introduce a natural subclass of meromorphic starlike functions in the open unit disk. Results concerning subordination properties, integral representations, properties of convolutions, inclusion relationship and coefficient inequalities for the functions of this class are derived. Furthermore, we solve radius problems for certain related classes of meromorphic strongly starlike functions and meromorphic parabolic starlike functions.

Convolutions of Harmonic Half-Plane Mappings with Harmonic Vertical Strip Mappings

Abstract: In the present paper, we prove the convolutions of generalized harmonic right half-plane mappings with harmonic vertical strip mappings are univalent and convex in the horizontal direction. Furthermore, we use a simple method to prove the Theorem~\ref{thmD} that has been proved Kumar~\cite[Theorem 2.4]{Kumar2}. Finally, some examples of harmonic univalent mappings convex in the horizontal direction are also constructed to illuminate our main results.

A note on convexity of convolutions of harmonic mappings

Abstract: . In this paper, we study right half-plane harmonic mappingsf 0 and f, where f 0 is xed and f is such that its dilatation of a conformalautomorphism of the unit disk. We obtain a sucient condition for theconvolution of such mappings to be convex in the direction of the realaxis. The result of the paper is a generalization of the result of by Li andPonnusamy [11], which itself originates from a problem posed by Dor etal. in [7]. 1. IntroductionLet D = fz2C : jzj<1gbe the unit disk. We will consider the family ofcomplex-valued harmonic mapping f= u+ ivde ned in a domain DˆC ifuand vare real harmonic in D, i.e., u= v= 0, where is the complexLaplacian operator = 4@ 2 @z@z:=@ 2 @x 2 +@@y 2 :Denote by Hthe class of all complex-valued harmonic mappings f in D nor-malized by f(0) = f z (0) 1 = 0. Let S H be the subclass of Hconsisting ofunivalent and sense-preserving functions. For a simply connected domain D,such functions can be written in the form f= h+ g, where(1) h(z) = z+X

Coefficient estimates for certain subclasses of analytic and bi-univalent functions

Abstract: For λ ≥ 0 and 0 ≤ α < 1 < β, we denote by K(λ,α,β) the class of normalized analytic functions satisfying the two sided-inequality α < K (Zf'(z)/f(z) + z2f''(z)/f(z))<β (z  U), where U is the open unit disk. Let KΣ (λ, α, β) be the class of bi-univalent functions such that f and its inverse f-1 both belong to the class K(λ, α, β). In this paper, we establish bounds for the coefficients, and solve the Fekete-Szegő problem, for the class K((λ,α,β). Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coefficients of the functions in the class KΣ (λ,α,β)

Certain subclass of analytic functions defined by means of differential subordination

Abstract: For $\alpha\in(\pi, \pi]$, let $\mathcal{R}_\alpha(\phi)$ denote the class of all normalized analytic functions in the open unit disk $\mathbb{U}$ satisfying the following differential subordination: $$f'(z)+\frac{1}{2}\left(1+e^{i\alpha}\right)zf''(z)\prec\phi(z)\qquad (z\in\mathbb{U}),$$ where the function $\phi(z)$ is analytic in the open unit disk $\mathbb{U}$ such that $\phi(0)=1$. In this paper, various integral and convolution characterizations, coefficient estimates and differential subordination results for functions belonging to the class $\mathcal{R}_\alpha(\phi)$ are investigated. The Fekete-Szeg\"{o} coefficient functional associated with the $k$th root transform $[f(z^k)]^{1/k}$ of functions in $\mathcal{R}_\alpha(\phi)$ is obtained. A similar problem for a corresponding class $\mathcal{R}_{\Sigma;\alpha}(\phi)$ of bi-univalent functions is also considered. Connections with previous known results are pointed out.

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

Abstract: In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk U that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered.

Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator

Abstract: In this paper, we investigate a new subclass Σn (τ , γ,φ) of analytic and bi-univalent functions in the open unit disk U defined by Salagean differential operator. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coeffi cient |a2| and |a3|.