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In this paper, we investigate the growth and fixed points of solutions of higher-order linear differential equations in the unit disc. We extend the coefficient conditions to a type of one-constant-control coefficient comparison and obtain the same estimates of iterated order of solutions. We also obtain better estimates by providing a precise value of iterated order of solution instead of a range of that in the case of coefficient characteristic function comparison. Moreover, we utilize iteration to investigate and estimate the fixed points of solutions’ arbitrary-order derivatives with higher-order equations f(k)+Ak−1(z)f(k−1)+⋯+A1(z)f′+A0(z)f=0 and provide a concise method to judge if the items generated by the iteration do not vanish identically and ensure the iteration proceeds. Our results are an improvement over those by B. Belaïdi, T. B. Cao, G. W. Zhang and A. Chen.

In this paper, we introduce and investigate two new subclasses H σ μ ( λ , φ ) and M σ γ ( λ , μ , φ ) of Ma-Minda bi-univalent functions defined by using subordination in the open unit disk D = { z ∈ C : | z | < 1 } . For functions belonging to these new subclasses, we obtain estimates for the initial coefficients | a 2 | and | a 3 | . The results presented in this paper would generalize those in related works of several earlier authors. MSC: 30C45, 30C80.

There are many articles in the literature dealing with differential subordination problems for analytic functions in the unit disk, and only a few articles deal with the above problems in the upper half-plane. In this paper, we aim to derive several differential subordination results for analytic functions in the upper half-plane by investigating certain suitable classes of admissible functions. Some useful consequences of our main results are also pointed out.

The main purpose of this paper is to derive some results associated with the quasi-Hadamard product of certain omega -starlike and omega -convex univalent analytic functions with respect to symmetric points.

Our aim in this paper is to deal with the growth property at infinity for modified Poisson integrals in an ...-dimensional cone. We also generalize the integral representation of harmonic functions in a half space of ... to the conical case. 2010 Mathematics Subject Classification: 31B10, 31C05 (ProQuest: ... denotes formulae omitted.)

An integral representation for a class of superfunctions, associated with the Schrödinger operator, is investigated. Meanwhile, growth properties of them are also proved outside of some exceptional sets. 2010Mathematics Subject Classification: 35J10, 35J25. Key words and phrases: Stationary Schrödinger operator, Poissona-integral, Greena-potential, Growth property, Integral representation, Cone.

In this paper, we introduce and investigate a new subclass M K ( k ) ( β , γ ) of meromorphic close-to-convex functions. For functions belonging to the class M K ( k ) ( β , γ ) , we obtain some coefficient inequalities and a distortion theorem. The results presented here would unify and extend some recent work of Wang et al. (Appl. Math. Lett. 25:454-460, 2012). MSC: 30C45.

In this article, a solution of the Dirichlet problem for the Schrödinger operator on a cone is constructed by the generalized Poisson integral with a slowly growing continuous boundary function. A solution of the Poisson integral for any continuous boundary function is also given explicitly by the Poisson integral with the generalized Poisson kernel depending on this boundary function. MSC: 31B05, 31B10.

We introduce new subclasses of close-to-convex and quasiconvex functions with respect to symmetric and conjugate points. The coefficient estimates for functions belonging to these classes are obtained.