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. In mathematics, a differential operator is an operator defined as a function of the differentiation operator. The differential operator can also be applied to other variables provided they are a function of x. For this subclass, the feketeszego type coefficient inequalities are derived. Also, since f0 0 and f 0 1, we have that b0 0 and bz 1. 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.
A new subclass of analytic functions defined by using. Applications of a qsalagean type operator on multivalent. A new class of analytic functions defined by using. For, salagean introduced the following differential operator.
On a new subclass of multivalent functions defined by. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found. This study not only in mathematics but extended to another topics. 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. When p e o and t o, opoola differential operator becomes al oboudi differential operator. 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. On starlike functions using the generalized salagean differential operator. This class is introduced by using the salagean q differential operator with the concept of janowski functions. Majorization properties for certain classes of analytic functions using the salagean operator. Differential subordinations and superordinations for analytic.
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. 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. Differential subordinations and superordinations for analytic functions defined by salagean integro differential operator. New classes containing ruscheweyh derivative and a new. On some classes of spirallike functions defined by the salagean operator. A new class of analytic functions defined by using salagean. 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. Majorization properties for certain new classes of analytic functions using the salagean operator. Pdf on new subclasses of biunivalent functions defined. Some differential subordinations using ruscheweyh derivative and salagean. Chapter 4 linear di erential operators in this chapter we will begin to take a more sophisticated approach to differential equations.
Majorization properties for certain new classes of analytic functions using the salagean operator, journal of inequalities and applications, 20, pp. Differential subordination results for certain integrodifferential operator and its applications kutbi, m. 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. Also, we consider the following differential operator. Many differential and integral operators can be written in term of convolution, for details we.
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. 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 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. Methods by taking motivation from the abovecited work, we introduce a new subclass u i,jq, b, a, b. 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. Second order differential operators and their eigenfunctions miguel a. In this paper, we introduce a new class kequation, equation, of multivalent functions using a newly defined qanalogue of a salagean type differential operator.
On the properties of a class of pvalent functions defined by. Some properties for integrodifferential operator defined by. 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 certain subclass of analytic functions based on. 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. A differential operator is an operator defined as a function of the differentiation operator.
Salagean differential operator, starlike functions, unit disk, univalent functions, analytic functions and subordination 1. This operator is a particular case of the operator defined in 3 and it is easy to see that for any. Pdf application of salagean differential operator to certain. Mathematics free fulltext a new subclass of analytic. In this paper, some properties such as a representation theorem and coefficient estimates for the class are obtained. 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. The introduction of differential operators allows to investigate differential equations in terms of.
Differential subordinations and superordinations for analytic functions defined by salagean integrodifferential operator. 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. On a class of univalent functions defined by salagean. Seoudy, on differential sandwich theorems of analytic functions defined by generalized salagean integral operator, applied mathematics letters 24 2011, pp. Geometric properties of a new integral operator bucur, roberta, andrei, loriana, and breaz, daniel, abstract and applied analysis, 2015. On a class of univalent functions defined by salagean differential.
By using this operator and the concept of the janowski function, we define certain new classes of analytic functions. On a class of univalent functions defined by salagean differential operator. Some notes on differential operators mit opencourseware. On subclass of analytic functions defined by generalised differential. Some differential subordinations using ruscheweyh derivative. The subclasses of univalent functions are defined using generalized differential operator studied by m. 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.
Functions based on an extension of salagean operator. Denote by u the open unit disc of the complex plane, u z c. Many properties have been discussed and studied many researchers for this two operators. In this manuscript, by using the salagean operator, new subclasses of biunivalent functions in the open unit disk are defined. His book linear partial differential operators published 1963 by springer in the grundlehren series was the first major account of this theory. Joseph olubunmi3 abstract let denote the class of function, analytic and univalent in the.
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. Pdf a new subclass of analytic functions defined by using. A new class of analytic functions associated with salagean operator. These are commonly expressed in terms of the symbol. Application of salagean differential operator to certain. A mode corresponds to what is known as an eigenfunction of the di. On certain subclasses of analytic and univalent functions. Then, for given by 1, we know that using this s l gean operator along. U, we introduce a class of holomorphic functions denoted by. In this paper, we introduce generalised differential operator. Subordination and superordination for multivalent functions associated with the dzioksrivastava operator. Multiplier differential operator s r swamy department of computer science and engineering, r v college of engineering, mysore road, bangalore560 059, india i.
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. Generalized briotbouquet differential equation by a quantum. Generalized briotbouquet differential equation by a. Second order differential operators and their eigenfunctions.
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. On certain subclass of analytic functions based on convolution of ruscheweyh and generalized salagean differential operator. Majorization properties for certain new classes of. For functions fz s, salagean 6 introduced a new differential operator called salagean differential operator dn defined by dn. Alonso the institute of optics, university of rochester. The analysis of linear partial differential operators iii pseudodifferential operators springerverlag berlin heidelberg newyork tokyo. On some classes of spirallike functions defined by the. Majorization properties for certain new classes of analytic. Pdf initial coefficients for a subclass of biunivalent functions. Majorization properties for certain new classes of analytic functions. Pdf a new subclass of analytic functions defined by.
Differential operator an overview sciencedirect topics. 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. Some properties of these classes are discussed, and numerous sharp results such as coef. It was followed by salagean 3 in 1983 giving another version of differential and integral operator.
When working with differential operators you use the same rules of differentiation to find the derivative of a function. We investigate the coefficient problem, feketeszego inequality, and some other properties related to subordination. 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. As a consequence, we deliver some interesting inclusions and inequalities of. John, on linear partial differential equations with analytic coefficients. 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 univalent functions defined by a generalized salagean operator. Ibrahim 1 which is generalization of well known salagean operator. It followed by salagean 2 in 1983 giving another version of differential and integral operator. A subclass of biunivalent functions defined by generalized. 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. Pdf a note on differential subordinations using salagean.
In this\ud paper, some properties such as a representation theorem and coefficient estimates for the class\ud are obtained. Hid four volume text the analysis of linear partial differential operators published in the same series 20 years later illustrates. A new subclass of analytic functions defined by using salagean q. On the properties of a class of pvalent functions defined. Certain subclass of analytic functions related with.
On a class of analytic functions associated to a complex domain. This operator is a particular case of the operator defined in. In our present investigation, we use the technique of convolution and quantum calculus to study the salagean qdifferential operator. Subordination and superordination for multivalent functions associated with. The d operator differential calculus maths reference. On a new subclass of biunivalent functions defined by using. 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. In particular, we will investigate what is required for a linear dif. An introduction to the linear differential operator. On a new subclass of multivalent functions defined by using. For example, when y is a function of x, its written as. For in 2, we obtain the salagean differential 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.
On starlike functions using the generalized salagean. However because y is a function of x you can still use the product rule to perform the differentiation. In our present investigation, we use the technique of convolution and quantum calculus to study the salagean q differential operator. On certain properties of pvalent functions defined by a. Many differential and integral operators can be recorded in terms of convolution, such as the salagean differential operator 6, aloboudi. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star. 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. The analysis of linear partial differential operators iii. As a consequence, we deliver some interesting inclusions and inequalities of these. Ruscheweyh 11 led the way in the theory of differential operators in 1975. Many articles discuss on operators and new generalizations of various authors. On a new subclass of multivalant functions defined by al.
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