Certain subclasses of multivalent functions involving linear operators (original) (raw)

Certain subclasses of multivalent functions associated with a family of linear operators

Mathematical and Computer Modelling, 2006

The main object of the present paper is to investigate a number of inclusion relationships and some other useful properties of several interesting subclasses of analytic and p-valent functions, which are defined here by means of a certain linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

Some Properties of Subclasses of Multivalent Functions

Abstract and Applied Analysis, 2011

The authors introduce two new subclasses denoted by and of the class of -valent analytic functions. They obtain coefficient inequality for the class . They investigate various properties of classes and . Furthermore, they derive partial sums associated with the class .

Some subclasses of multivalent functions involving a certain linear operator

Journal of Mathematical Analysis and Applications, 2005

The authors investigate various inclusion and other properties of several subclasses of the class A p of normalized p-valent analytic functions in the open unit disk, which are defined here by means of a certain linear operator. Problems involving generalized neighborhoods of analytic functions in the class A p are investigated. Finally, some applications of fractional calculus operators are considered.

Certain Classes of Multivalent Functions Related with a Linear Operator

Acta Universitatis Apulensis, 2011

Abstract. In this paper, we introduce and study some new classes of analytic functions using a convolution operator L∗ p (a, c): A→ A. Some inclusion relationships and a radius problem are investigated. We also show that the class Rk, p (a, c, α) is closed under convolution ...

Geometric Properties And Neighborhood For Certain Subclasses Of Multivalent Functions

2017

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

A Class of Multivalent Functions Involving a Generalized Linear Operator and Subordination

2010

In this manuscript, a class of multivalent functions defined in terms of a linear multiplier operator containing the generalized Komatu integral operator is introduced and investigated. The main results of inclusion relation, integral preserving property, argument estimate and subordination property are proved by making use of subordination formulas between analytic functions.

Some families of linear operators associated with certain subclasses of multivalent functions

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.