Dor 3 although, some results on convolution of harmonic functions are available in literature, but still very little is known in this direction. Convolution properties of these classes which include the classical classes of starlike, convex, closetoconvex, and quasiconvex analytic functions are investigated. Research article inclusion properties of new classes of. Relevant connections of the results presented here with those obtained in earlier works are pointed out. Singh, convolution properties of some classes of analytic functions j. In one dimension the convolution between two functions, fx and hx. 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. J,e of analytic functions defined by using the wright function with the operator d w o,p. Pdf making use of convolution, we introduce and investigate a certain class of functions which is analytic in the open unit disk. Some classes of panalytic functions defined by certain.
Making use of a convolution structure, we introduce a new class of analytic functions pt g. We start by giving some preliminaries for a better understanding of the research work to follow. As can be seen the operation of continuous time convolution has several important properties that have been listed and proven in this module. An interesting criterion was given by ponnusamy and singh s. Some convolution properties of multivalent analytic functions. 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. 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. Singh, convolution properties of some classes of analytic functions, internal report,spicscience foundation, 1990. Zayed department of mathematics, faculty of science. Properties of a generalized class of analytic functions with. Research article convolution properties for some subclasses of meromorphic functions of complex order m. Let pdenote the wellknown class of carath eodory functions psuch that p2hu, with p0 1 and repz 0, z 2u.
Some convolution properties and radii problems are investigated. Some properties of a new class of analytic functions. 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. Some convolution properties of a certain class of pvalent. Convolution properties of classes of analytic and meromorphic. Some geometric properties of analytic functions associated. Kand qare the wellknown classes of starlike, convex, closetoconvex and quasiconvex functions respectively. 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. Convolution properties for certain classes of analytic functions. Conversely, by puiseuxs theorem the zero set of a real analytic function. The study of operators plays a vital role in mathematics. 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.
We also indicate relevant connections of the various results presented in this. Some geometric properties of analytic functions associated with hypergeometric functions kassim a. Pdf ruscheweyh and sheilsmall proved the polyaschoenberg conjecture. Several properties like, the coefficient bounds, growth. For example, in the case of the graph of y hxn1 one can take. Convolution properties for certain classes of analytic. Convolution properties of subclasses of analytic functions associated with the dzioksrivastava operator s. We investigate convolution properties and coefficients estimates for two classes of analytic functions involving the derivative operator defined. 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. In this investigation, motivated from breaz study, we introduce a new family of integral operator using famous convolution technique. On certain subclasses of closetoconvex functions related with the.
Convolution operators in the geometric function theory. 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. We introduce several inclusion properties of the new kuniformly classes us d. Convolution properties dsp for scientists department of physics university of houston. Generalized convolution properties for certain classes of. General classes of analytic functions defined by convolution with a fixed analytic function are introduced. We also apply this newly defined operator for investigating some interesting mapping properties of certain subclasses of analytic and univalent functions. Convolution properties for some subclasses of meromorphic. Pdf extreme points and convolution properties of some. Jun, 2010 general classes of analytic functions defined by convolution with a fixed analytic function are introduced. Also, some another interesting properties of the class. Some convolution properties of certain classes of analytic functions khalida inayat noora, nak eun chob. Convolution properties for some subclasses of meromorphic bounded functions of complex order a. In fact any such curve is part of the zeroset of a real analytic function.
Beerendss fourier and laplace transforms and applying the definition to these examples gave the result. Some classes of panalytic functions defined by certain integral operator author. Some properties of an integral operator defined by convolution. Other analytic classes of fractional power are studied by the authors as well see 79. A framework for constructing sets without configurations robert fraser. Some convolution properties for the classes of bounded qstarlike and qconvex univalent functions of complex order were investigated by aouf and seoudy 4. These operators are defined by using convolution of normalized analytic functions and hypergeometric functions, where several interesting results are obtained see also 10, 11. Department of mathematics abbottabad university of science and technology abbottabad, pakistan. Goyal, sanjay kumar bansal, pranay goswami, zhigang wang submitted by. For these classes inclusion relations are studied mainly using the method of differential subordination. Zayed 2 department of mathematics, faculty of science, mansoura university, mansoura, egypt. 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. Some convolution properties of certain classes of analytic. Nazar khan, bilal khan, qazi zahoor ahmad, sarfraz ahmad.
Singh, convolution properties of some classes of analytic functions, internal report, spic science foundation, 1990. These classes are shown to be closed under convolution with prestarlike functions and the bernardilibera integral. Similar convolution results for two classes of analytic functions are also obtained. Explaining convolution using matlab thomas murphy1 abstract students often have a difficult time understanding what convolution is.
Some domination properties of the total graph of a module with respect to singular submodule jituparna goswami. Convolution properties of convex harmonic functions. In one dimension the convolution between two functions, fx and hx is dened as. Convolutions for certain analytic functions 1 introduction emis. A discrete convolution can be defined for functions on the set of. In this present paper, some interesting convolution properties of functions fz in the classes sd. Let a denote the class of functions which are analytic in z class of functions f such thatref. On some classes of spirallike functions defined by the. By using the principle of differential subordination, we introduce subclass of pvalent meromorphic functions involving convolution and investigate various properties for this subclass. Convolution and subordination properties of analytic. Research article convolution properties for some subclasses. Biunivalent properties for certain class of bazilevic. We also indicate relevant connections of the various results presented in this paper with the obtained results in earlier works.
Convolution properties of these classes which include the classical classes of starlike. 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. Singh, convolution properties of some classes of analytic functions, j. Some geometric properties of a family of analytic functions. Subordination and convolution properties of subclasses of. Convolution kernels of 2d fourier multipliers based on real. In fact the convolution property is what really makes fourier methods useful. Pdf convolution properties of classes of analytic and. Convolution properties of some classes of analytic functions. Convolution properties of subclasses of analytic functions.
Some convolution properties of analytic functions request pdf. The convolution can be defined for functions on euclidean space, and other groups. We investigate convolution properties and coefficients estimates for two classes of analytic functions involving the q derivative operator defined in the open unit disc. Convolution conditions for the qanalogue classes of janowski functions hamid shamsan and s. The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the dzioksrivastava. Pdf some properties of a class of analytic functions researchgate.
Some applications of differential subordination to certain. 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. Functions on real line dt signal model functions on integers system properties lti causal etc ch. The class of univalent functions is represented by sand it is a subclass of the class a, whereas, s. Set and we note that from the identity and the fact that the result follows from theorem 1. 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. Taking in theorem 1, we obtain the following result which improves the result of aouf and seoudy 23, theorem 2. Convolution properties of classes of analytic and meromorphic functions. The function defined by 1 is in the class if and only if for all and also.
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