Then, for given by 1, we know that using this s l gean operator along. On certain subclasses of analytic and univalent functions. When working with differential operators you use the same rules of differentiation to find the derivative of a function. Pdf on apr 11, 2018, evrim toklu and others published on new subclasses of biunivalent functions defined by generalized salagean differential operator find, read and cite all the research. For example, when y is a function of x, its written as.
When p e o and t o, opoola differential operator becomes al oboudi differential operator. Interior regularity and local existence theorems 4. Pdf a note on differential subordinations using salagean. The d operator differential calculus maths reference. We investigate the coefficient problem, feketeszego inequality, and some other properties related to subordination. Subordination and superordination for multivalent functions associated with. For this subclass, the feketeszego type coefficient inequalities are derived. On a class of univalent functions defined by salagean differential operator.
On some classes of spirallike functions defined by the salagean operator. In this\ud paper, some properties such as a representation theorem and coefficient estimates for the class\ud are obtained. Many differential and integral operators can be recorded in terms of convolution, such as the salagean differential operator 6, aloboudi. Some results for the class of analytic functions involving salagean differential operator beberapa sifat untuk kelas fungsi analisis melibatkan pengoperasi pembeza salagean alawiah ibrahim1, maslina darus1, sever s. Subordination and superordination for multivalent functions associated with the dzioksrivastava operator. Ibrahim 1 which is generalization of well known salagean operator. A note on differential subordinations using salagean and ruscheweyh operators article pdf available in libertas mathematica 61 january 2010 with 82 reads how we measure reads. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found. The pdf file you selected should load here if your web browser has a pdf reader plugin installed for example, a recent version of adobe acrobat reader if you would like more information about how to print, save, and work with pdfs, highwire press provides a helpful frequently asked questions about pdfs alternatively, you can download the pdf file directly to your computer, from where it. John, on linear partial differential equations with analytic coefficients. One way to understand the symbol of a differential operator or more generally, a pseudodifferential operator is to see what the operator does to wave packets functions that are strongly localised in both space and frequency. In this paper, some properties such as a representation theorem and coefficient estimates for the class are obtained. Differential subordination results for certain integrodifferential operator and its applications kutbi, m.
Some properties of these classes are discussed, and numerous sharp results such as coef. On univalent functions defined by a generalized salagean operator. For in 2, we obtain the salagean differential operator. On some classes of spirallike functions defined by the. Chapter 4 linear di erential operators in this chapter we will begin to take a more sophisticated approach to differential equations. Mar 14, 2020 in the present study, we employ the concept of quantum calculus and the convolution product to impose a generalized symmetric salagean qdifferential operator. New classes containing ruscheweyh derivative and a new. Applications of a qsalagean type operator on multivalent.
In 2004, aloboudi 3 generalized salagean operator followed by s. Some results for the class of analytic functions involving. On a new subclass of multivalant functions defined by al. Differential operator an overview sciencedirect topics. In mathematics, a differential operator is an operator defined as a function of the differentiation operator. In our present investigation, we use the technique of convolution and quantum calculus to study the salagean qdifferential operator. Also, we consider the following differential operator. The pdf file you selected should load here if your web browser has a pdf reader plugin installed for example, a recent version of adobe acrobat reader if you would like more information about how to print, save, and work with pdfs, highwire press provides a helpful frequently asked questions about pdfs. In particular, we will investigate what is required for a linear dif. By using this operator and the concept of the janowski function, we define certain new classes of analytic functions. Majorization properties for certain new classes of analytic.
It was followed by salagean 3 in 1983 giving another version of differential and integral operator. Hid four volume text the analysis of linear partial differential operators published in the same series 20 years later illustrates the vast expansion of the subject in that period. Pdf applications of salagean differential operator at the class of. On starlike functions using the generalized salagean. Terwase department of mathematics, faculty of physical sciences, plateau state university, bokkos, nigeria abstract in this paper, we obtain certain properties of an operator defined by the convolution between ruscheweyh and salagean differential operator. A new subclass of analytic functions defined by using. This study not only in mathematics but extended to another topics. This operator is a particular case of the operator defined in 3 and it is easy to see that for any. Salagean differential operator, starlike functions, unit disk, univalent functions, analytic functions and subordination 1. On starlike functions using the generalized salagean differential operator. By using the generalized salagean differential operator, we introduce a class of pharmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.
Majorization properties for certain new classes of. Ruscheweyh 11 led the way in the theory of differential operators in 1975. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star. Some results for the class of analytic functions involving salagean differential operator 93 2 1 1 1 z d fz d f z b z z n n n for any z u. Some properties for integrodifferential operator defined by. Application of salagean differential operator to certain. Differential subordinations and superordinations for analytic functions defined by salagean integro differential operator. Denote by u the open unit disc of the complex plane, u z c. Differential subordinations and superordinations for analytic functions defined by salagean integrodifferential operator. Functions based on an extension of salagean operator. Let \ud denote the class of function\ud, analytic and univalent in the\ud open unit disk, which are defined involving the salagean differential\ud operator, such that.
For functions fz s, salagean 6 introduced a new differential operator called salagean differential operator dn defined by dn. In this paper, we introduce generalised differential operator. A new class of analytic functions defined by using salagean. On a new subclass of multivalent functions defined by using. In this effort, we investigate a generalized integrodifferential operator m z defined by a fractional formal fractional differential operator and study some its geometric properties by employing it in new subclasses of analytic univalent functions. Alonso the institute of optics, university of rochester. They constitute the most complete and uptodate account of this subject, by the author who has dominated it and made the most significant contributions in the last decadesit is a superb book. Pdf a new subclass of analytic functions defined by using. Some differential subordinations using ruscheweyh derivative and salagean operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function in the style of a higherorder function in computer science this article considers mainly linear operators, which are the most. Geometric properties of a new integral operator bucur, roberta, andrei, loriana, and breaz, daniel, abstract and applied analysis, 2015. On the properties of a class of pvalent functions defined. A a, n n n d fz dd fz, n d fz dfz zf z d fz fz n 1 1 the basic classes of convex functions, starlike functions, functions with negative coefficients and many other. Also, since f0 0 and f 0 1, we have that b0 0 and bz 1.
Generalized briotbouquet differential equation by a. For two functions and, analytic in, we say that the function is subordinate to in and write, if there exists a schwarz function, which by definition is analytic in with and, such that. Differential subordinations and superordinations for analytic. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another in the style of a higherorder function in computer science. Generalized briotbouquet differential equation by a quantum.
Second order differential operators and their eigenfunctions. Second order differential operators and their eigenfunctions miguel a. Some differential subordinations using ruscheweyh derivative and salagean. In this paper, we introduce two subclasses of analytic and spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and. On certain subclass of analytic functions based on convolution of ruscheweyh and generalized salagean differential operator.
A new class of analytic functions associated with salagean operator. A differential operator is an operator defined as a function of the differentiation operator. The aim of this paper is to study certain subclasses of biunivalent functions defined by generalized salagean differential operator related to shelllike curves connected with fibonacci numbers. On a class of analytic functions associated to a complex domain. Pdf a new subclass of analytic functions defined by. On a new subclass of multivalent functions defined by. Mathematics free fulltext a new subclass of analytic. Let \ud denote the class of function\ud, analytic and univalent in the\ud open unit disk, which are defined involving the salagean differential \ud operator, such that. The differential operator grad operates on a scalar field to produce a vector field, while the operators div and curl operate on a vector field, producing a scalar field and a vector field, respectively. In this paper, we introduce a new class kequation, equation, of multivalent functions using a newly defined qanalogue of a salagean type differential operator. As a consequence, we deliver some interesting inclusions and inequalities of. A new subclass of analytic functions defined by using salagean q.
Many properties have been discussed and studied many researchers for this two operators. The subclasses of univalent functions are defined using generalized differential operator studied by m. Joseph olubunmi3 abstract let denote the class of function, analytic and univalent in the. On a class of univalent functions defined by salagean differential.
These are commonly expressed in terms of the symbol. A subclass of biunivalent functions defined by generalized. A mode corresponds to what is known as an eigenfunction of the di. The introduction of differential operators allows to investigate differential equations in terms of. Hid four volume text the analysis of linear partial differential operators published in the same series 20 years later illustrates. By consuming the new operator and the model of the janowski function, we describe definite new classes of analytic functions in the open unit disk. On certain subclass of analytic functions based on. This operator is a particular case of the operator defined in. On the properties of a class of pvalent functions defined by. Certain subclass of analytic functions related with. Many differential and integral operators can be written in term of convolution, for details we. Some differential subordinations using ruscheweyh derivative.
Some notes on differential operators mit opencourseware. Some notes on differential operators a introduction in part 1 of our course, we introduced the symbol d to denote a func tion which mapped functions into their derivatives. On a new subclass of biunivalent functions defined by using. The analysis of linear partial differential operators iii pseudodifferential operators springerverlag berlin heidelberg newyork tokyo. However because y is a function of x you can still use the product rule to perform the differentiation. Majorization properties for certain new classes of analytic functions using the salagean operator, journal of inequalities and applications, 20, pp. In other words, the domain of d was the set of all differentiable functions and the image of d was the set of derivatives of these differentiable func tions. For, salagean introduced the following differential operator. Linear differential operators 5 for the more general case 17, we begin by noting that to say the polynomial pd has the number aas an sfold zero is the same as saying pd has a factorization. The analysis of linear partial differential operators iii. Many articles discuss on operators and new generalizations of various authors.
This class is introduced by using the salagean q differential operator with the concept of janowski functions. Pdf on new subclasses of biunivalent functions defined. Majorization properties for certain classes of analytic functions using the salagean operator. On a class of univalent functions defined by salagean differential operator article pdf available in banach journal of mathematical analysis 32009 january 2009 with 300 reads. The differential operator can also be applied to other variables provided they are a function of x.
In this manuscript, by using the salagean operator, new subclasses of biunivalent functions in the open unit disk are defined. Differential subordinations and superordinations for. Majorization properties for certain new classes of analytic functions. Multiplier differential operator s r swamy department of computer science and engineering, r v college of engineering, mysore road, bangalore560 059, india i. A new class of analytic functions defined by using. His book linear partial differential operators published 1963 by springer in the grundlehren series was the first major account of this theory. Seoudy, on differential sandwich theorems of analytic functions defined by generalized salagean integral operator, applied mathematics letters 24 2011, pp. Methods by taking motivation from the abovecited work, we introduce a new subclass u i,jq, b, a, b. On certain properties of pvalent functions defined by a. An introduction to the linear differential operator. Majorization properties for certain new classes of analytic functions using the salagean operator.
On a class of univalent functions defined by salagean. Pdf initial coefficients for a subclass of biunivalent functions. U, we introduce a class of holomorphic functions denoted by. It followed by salagean 2 in 1983 giving another version of differential and integral operator. Let denote the class of function, analytic and univalent in the open unit disk, which are defined involving the salagean differential operator, such that. On subclass of analytic functions defined by generalised differential. Pdf application of salagean differential operator to certain.
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