Some relations including various linear operators

J. Inequal. Pure Appl. Math, 2008

In this paper we introduce a new class H(φ, α, β) of analytic functions which is defined by means of a Hadamard product (or convolution) of two suitably normalized analytic functions. Several properties like, the coefficient bounds, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are investigated. We further consider a subordination theorem, certain boundedness properties associated with partial sums, an integral transform of a certain class of functions, and some integral means inequalities. Several interesting consequnces of our main results are also pointed out.

Applied Mathematics and Computation, 2008

In this paper, we give an extension of the Ö zkan and Altintas ß results [Ö . Ö zkan, O. Altintas ß, Applications of differential subordination, Appl. Math. Lett. 19 (2006) 728-734] on the inclusion relationships involving various subclasses of analytic and univalent functions, defined in terms of linear operators. We show that these classes are closed under convolution with convex functions.

Mathematica

Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these operators, we define and study new classes of functions in the unit disk. Moreover, we obtain some basic properties of the new classes, namely inclusion, growth, covering, distortion, closure under certain integral transformation and coefficient inequalities. Comment: 10 pages. Published

AIP Conference Proceedings, 2019

The purpose of the present paper is to introduce new operator using the Salagean operator and Ruscheweyh operator for analytic functions. We study the differential subordinations in the general case and investigate differential subordination properties regarding the operator. Moreover, we determine dominants and best dominants of differential subordinations integral operators are also considered.

Journal of Applied Analysis, 2000

In this paper we consider the Hadamard product of regular functions using the concept of subordination. Let P (A, B) denote the class of regular functions subordinated to the linear fractional transfor-

Journal of the Egyptian Mathematical Society, 2014

In this paper the author established certain results concerning the quasi-Hadamard product for generalized subclasses of p-valent functions with positive coefficients.

Computers & Mathematics with Applications, 2008

Making use of a certain linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce two novel subclasses P a,c (A, B; p, λ) and P + a,c (A, B; p, λ) of the class A(p) of normalized p-valent analytic functions in the open unit disk. The main objective of the present paper is to investigate the various important properties and characteristics of each of these subclasses. Furthermore, several properties involving neighborhoods of functions in these subclasses are investigated. We also derive many results for the modified Hadamard products of functions belonging to the class P + a,c (A, B; p, λ). Finally, some applications of fractional calculus operators are considered.

Annales Polonici Mathematici, 2002

A certain general class S(a, c, A, B) of analytic functions involving a linear operator is introduced. The objective is to investigate various properties and characteristics of this class. Several applications of the results (obtained here) to a class of fractional calculus operators are also considered. The results contain some of the earlier work in univalent function theory.

2019

The object of this paper is to give some applications of differential subordination concept on subclasses of univalent functions for some convolution operators which are defined on the space of univalent meromorphic functions in the punctured open unit disc. Moreover, we derive some sandwich theorems, we study some geometric properties like coefficient bounds, distortion theorem, and radii of starlikeness and convexity for these classes of functions. Extreme points and integral operator are also investigated.

Journal of Mathematics and Statistics

Problem statement: We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to wellknown results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.