Some convolution properties for the classes of bounded qstarlike and qconvex univalent functions of complex order were investigated by aouf and seoudy 4. Beerendss fourier and laplace transforms and applying the definition to these examples gave the result. Pdf extreme points and convolution properties of some. Convolution properties of these classes which include the classical classes of starlike.
Pdf some properties of a class of analytic functions researchgate. Convolutions for certain analytic functions 1 introduction emis. Convolution properties for some subclasses of meromorphic. Zayed department of mathematics, faculty of science. Kand qare the wellknown classes of starlike, convex, closetoconvex and quasiconvex functions respectively. Some convolution properties of analytic functions request pdf. Padmanabhanon analytic functions with reference to. Convolution properties of these classes which include the classical classes of starlike, convex, closetoconvex, and quasiconvex analytic functions are investigated.
Convolution properties for certain classes of analytic. Zayed 2 department of mathematics, faculty of science, mansoura university, mansoura, egypt. The class of univalent functions is represented by sand it is a subclass of the class a, whereas, s. Singh, convolution properties of some classes of analytic functions, internal report,spicscience foundation, 1990. Convolution properties of subclasses of analytic functions associated with the dzioksrivastava operator s. Students can often evaluate the convolution integral continuous time case, convolution sum discretetime case, or perform graphical convolution but may not have a good grasp of what is happening. Certain classes of analytic functions with negative. Research article inclusion properties of new classes of.
Some geometric properties of analytic functions associated. Singh, convolution properties of some classes of analytic functions, internal report, spic science foundation, 1990. Department of mathematics abbottabad university of science and technology abbottabad, pakistan. Convolution properties for certain classes of analytic functions. Relevant connections of the results presented here with those obtained in earlier works are pointed out. Pdf ruscheweyh and sheilsmall proved the polyaschoenberg conjecture. With slight modifications to proofs, most of these also extend to continuous time circular convolution as well and the cases in which exceptions occur have been noted above. The current article introduces a class of analytic functions with help of a generalized integral operator and discusses some useful convolution properties for this family in the lemniscate of bernoulli domain. We also indicate relevant connections of the various results presented in this paper with the obtained results in earlier works. Dor 3 although, some results on convolution of harmonic functions are available in literature, but still very little is known in this direction.
Convolution is the process by which an input interacts with an lti system to produce an output convolut ion between of an input signal x n with a system having impulse response hn is given as, where denotes the convolution f k f x n h n x k h n k. Some geometric properties of a family of analytic functions. We introduce several inclusion properties of the new kuniformly classes us d. The convolution operators induced by kernels satisfying a smoothness condition near the origin are shown to have asymptotic behaviour that matches that of powers of v, and a new class of convolution operators that are not nilpotent, but have kernels that are not polynomial generators for l1p 0. We also apply this newly defined operator for investigating some interesting mapping properties of certain subclasses of analytic and univalent functions. Making use of the operator for functions of the form, which are analytic in the punctured unit disc and, we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses. Generalized convolution properties for certain classes of. We investigate convolution properties and coefficients estimates for two classes of analytic functions involving the derivative operator defined. To define an operator using the convolution theory, and then study its properties, is one of the hot areas of current ongoing research in the geometric function theory and its related fields.
In this present paper, some interesting convolution properties of functions fz in the classes sd. Some domination properties of the total graph of a module with respect to singular submodule jituparna goswami. By using the principle of differential subordination, we introduce subclass of pvalent meromorphic functions involving convolution and investigate various properties for this subclass. Convolution conditions for the qanalogue classes of janowski functions hamid shamsan and s. These operators are defined by using convolution of normalized analytic functions and hypergeometric functions, where several interesting results are obtained see also 10, 11. Convolution properties for some subclasses of meromorphic bounded functions of complex order a. Singh, convolution properties of some classes of analytic functions j. Some properties of a new class of analytic functions. In the present paper, we obtain some inclusion relations and convolution properties for certain subclasses of analytic functions in the unit disk which are defined by the generalized salagean operator. Making use of a convolution structure, we introduce a new class of analytic functions pt g. The object of the present paper is to derive some properties of certain general class sn,p a, b of multivalent analytic functions involving a linear operator in the open unit disk. Convolution properties of convex harmonic functions 71 then, both f andf belong to k0 h, but their convolution f f is not even univalent in e for n 3 see m.
In one dimension the convolution between two functions, fx and hx. J,e of analytic functions defined by using the wright function with the operator d w o,p. Some properties of an integral operator defined by convolution. Some classes of panalytic functions defined by certain.
General classes of analytic functions defined by convolution with a fixed analytic function are introduced. Research article convolution properties for some subclasses. For combinatorialists, generating functions make the proof of certain combinatorial identities so easy in some cases that there are various combinatorial identities whose only proofs are via generating functions and for which a combinatorial proof isnt known. Some geometric properties of analytic functions associated with hypergeometric functions kassim a. Let a denote the class of functions which are analytic in z class of functions f such thatref. Some convolution properties of certain classes of analytic. Convolution properties of classes of analytic and meromorphic. Some applications of differential subordination to certain.
Convolution kernels of 2d fourier multipliers based on real. In fact the convolution property is what really makes fourier methods useful. Similar convolution results for two classes of analytic functions are also obtained. Goyal, sanjay kumar bansal, pranay goswami, zhigang wang submitted by.
An interesting criterion was given by ponnusamy and singh s. We start by giving some preliminaries for a better understanding of the research work to follow. For these classes inclusion relations are studied mainly using the method of differential subordination. Conversely, by puiseuxs theorem the zero set of a real analytic function. Some convolution properties and radii problems are investigated. Taking in theorem 1, we obtain the following result which improves the result of aouf and seoudy 23, theorem 2. For example, in the case of the graph of y hxn1 one can take. Some classes of panalytic functions defined by certain integral operator author. Convolution properties of subclasses of analytic functions. We also indicate relevant connections of the various results presented in this.
Jun, 2010 general classes of analytic functions defined by convolution with a fixed analytic function are introduced. Subordination and convolution properties of subclasses of. Biunivalent properties for certain class of bazilevic. Nazar khan, bilal khan, qazi zahoor ahmad, sarfraz ahmad. As can be seen the operation of continuous time convolution has several important properties that have been listed and proven in this module. These classes are shown to be closed under convolution with prestarlike functions and the bernardilibera integral. Several properties like, the coefficient bounds, growth.
On some classes of spirallike functions defined by the. A discrete convolution can be defined for functions on the set of. The convolution can be defined for functions on euclidean space, and other groups. Jassim department of mathematics, college of science, university of baghdad, baghdad, iraq abstract we presented in this paper a new class containing analytic univalent functions defined on unit disk. Pdf making use of convolution, we introduce and investigate a certain class of functions which is analytic in the open unit disk. Convolution properties of convex harmonic functions. Research article convolution properties for some subclasses of meromorphic functions of complex order m. Some convolution properties of certain classes of analytic functions khalida inayat noora, nak eun chob. In fact any such curve is part of the zeroset of a real analytic function. Using these integral operators, certain subclasses of analytic functions related to starlike functions, convex functions, close to convex functions, strongly starlike and strongly convex functions of order, are defined. The object of this paper is to introduce new subclass of bazilevic functions for the class \\sum \ with bounded boundary rotation and defined by using convolution as follows.
In this investigation, motivated from breaz study, we introduce a new family of integral operator using famous convolution technique. Set and we note that from the identity and the fact that the result follows from theorem 1. We investigate convolution properties and coefficients estimates for two classes of analytic functions involving the q derivative operator defined in the open unit disc. Functions on real line dt signal model functions on integers system properties lti causal etc ch. Also, some another interesting properties of the class. In one dimension the convolution between two functions, fx and hx is dened as. Convolution properties dsp for scientists department of physics university of houston. Let pdenote the wellknown class of carath eodory functions psuch that p2hu, with p0 1 and repz 0, z 2u. Aouf department of mathematics, faculty of science, mansoura university, mansoura 35516, egypt email. Some convolution properties of a certain class of pvalent. Some convolution properties of multivalent analytic functions. Convolution and subordination properties of analytic.
Properties of a generalized class of analytic functions with. The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the dzioksrivastava. Pdf convolution of certain analytic functions researchgate. Convolution properties of classes of analytic and meromorphic functions. Explaining convolution using matlab thomas murphy1 abstract students often have a difficult time understanding what convolution is. Convolution properties of some classes of analytic functions. The study of operators plays a vital role in mathematics. Singh, convolution properties of some classes of analytic functions, j. The function defined by 1 is in the class if and only if for all and also. Other analytic classes of fractional power are studied by the authors as well see 79. A framework for constructing sets without configurations robert fraser. Pdf convolution properties of classes of analytic and. In this surveytype article, we discuss historic development and exploit the strengths and properties of some differential and integral. On certain subclasses of closetoconvex functions related with the.