On a Subordination Theorem for a Class of Meromorphic Functions (original) (raw)

Sufficient Conditions for Subordination of Meromorphic Functions

Journal of Mathematics and Statistics, 2009

Problem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various researchers. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, by having new operators, new criteria and new set of subordination theorems could be obtained with some earlier results and standard methods.

Subordination and superordination of certain linear operator on meromorphic functions

Annales UMCS, Mathematica, 2010

Using the methods of differential subordination and superordination, sufficient conditions are determined on the differential linear operator of meromorphic functions in the punctured unit disk to obtain, respectively, the best dominant and the best subordinant. New sandwich-type results are also obtained. 1. Introduction. Let H(U) be the class of functions analytic in U = {z : z ∈ C and |z| < 1} and H[a, n] be the subclass of H(U) consisting of functions of the form f (z) = a + a n z n + a n+1 z n+1 +. .. , with H = H[1, 1]. Let f and F be members of H(U). The function f is said to be subordinate to F , or F is said to be superordinate to f , if there exists a function ω analytic in U with ω(0) = 0 and |ω(z)| < 1 (z ∈ U), such that f (z) = F (ω(z)). In such a case we write f (z) ≺ F (z). If F is univalent, then f (z) ≺ F (z) if and only if f (0) = F (0) and f (U) ⊂ F (U) (see [5] and [6]). Denote by Q the set of all functions q(z) that are analytic and injective onŪ \E(q) where E(q) = ζ ∈ ∂U : lim z→ζ q(z) = ∞ ,

A Study of Distortion Theorem and Inclusion Relations for a new class of Meromorphic Functions

IOSR Journals , 2019

By having used of differential subordination, it has been investigated in the present paper, subordination relations, inclusion relations, distortion theorem and inequality properties are discussed of the class𝕄𝔹(𝜶, 𝝀, 𝓵,𝝁, 𝜜, 𝜝). In this paper it has been introduced some new classes 𝕄𝔹(𝜶, 𝝀, 𝓵, 𝝁, 𝜜, 𝜝) of meromorphic functions which are defined by means a meromorphic function using a new operator.

Coefficient bounds for certain subclasses for meromorphic functions involving quasi subordination

THE 2ND UNIVERSITAS LAMPUNG INTERNATIONAL CONFERENCE ON SCIENCE, TECHNOLOGY, AND ENVIRONMENT (ULICoSTE) 2021

In the present paper, the authors introduce and investigates two new subclasses  and  of meromorphic functions which are defined by terms of the quasi-subordination. The coefficients estimate inclusive of the classical Fekete-Szegö functional| |for functions belonging to this class are then derived. Investigate a majorization problem for the class's meromorphic functions associated with these classes is also pointed out.

The Fekete-Szego inequalities for meromorphic functions associated with quasi-subordination

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation

The bounds for the Fekete-Szegö coefficient functional associated with quasi-subordination for subclasses of meromorphic functions f defined on the open unit disk in the complex plane are obtained.

Application of Quasisubordination to Certain Classes of Meromorphic Functions

Journal of Function Spaces, 2020

Inequalities play a fundamental role in many branches of mathematics and particularly in real analysis. By using inequalities, we can find extrema, point of inflection, and monotonic behavior of real functions. Subordination and quasisubordination are important tools used in complex analysis as an alternate of inequalities. In this article, we introduce and systematically study certain new classes of meromorphic functions using quasisubordination and Bessel function. We explore various inequalities related with the famous Fekete-Szego inequality. We also point out a number of important corollaries.