Convolution, coefficient and radius problems of certain univalent functions [QA331. M231 2009 f rb].

Dengan menggunakan ciri-ciri konvolusi dan teori subordinasi, beberapa subkelas fungsi meromorfi diperkenalkan. By making use of the properties of convolution and theory of subordination, several subclasses of meromorphic functions are introduced

Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out

On a Certain Subclass of Meromorphic Functions Defined by a New Linear Differential Operator

In this article, a new linear differential operator I^k (L_s^a (a_l,b_m )f(z)) is defined by using the Hadamard product of the q-hypergeometric function and a function related to the Hurwitz-Lerch zeta function. By using this linear differential operator, a new subclass L_(s,a)^(k,*) (α_l,β_m;A,B,b) of meromorphic functions is defined. Some properties and characteristics of this subclass are considered. These include the coefficient inequalities, the growth and distortion properties and the radii of meromorphic starlikeness and meromorphic convexity. Finally, closure theorems and extreme points are introduced

Differential Subordination For Meromorphic Functions Defined By A Linear Operator.

By making use of a linear operator that is defined by means of the Hadamard product (or convolution), we investigate the properties of a certain family of meromorphically multivalent functions

A certain subclass of univalent meromorphic functions defined by a linear operator associated with the Hurwitz-Lerch zeta function

In this paper, we study a linear operator related to Hurwitz-Lerch zeta function and hypergeometric function in the punctured unit disk. A certain subclass of meromorphically univalent functions associated with the above operator defined by the concept of subordination is also introduced, and its characteristic properties are studied

Differential Subordination And Superordination For Analytic And Meromorphic Functions Defined By Linear Operators [QA331. N219 2007 f rb].

Suatu fungsi f yang tertakrif pada cakera unit terbuka U dalam satah kompleks C disebut univalen jika fungsi tersebut memetakan titik berlainan dalam U ke titik berlainan dalam C. A function f defined on the open unit disk U of the complex plane C is univalent if it maps different points of U to different points of C

Convolution And Coefficient Problems For Multivalent Functions Defined By Subordination

Andaikan C satah kompleks, U = {z E C : Izl < I} cakera unit terbuka dalam C dan H(U) kelas fungsi analisis dalam U. Andaikan juga A kelas fungsi analisis 1 dalam U yang ternormalkan dengan 1(0) = 0 dan 1'(0) = 1. Fungsi 1 E A mempunyai siri Taylor berbentuk 00 l(z) = z + L anzn, (z E U). n=2 Andaikan Ap (p EN) kelas fungsi analisis 1 berbentuk 00 1(z) = zP + L anzn, (z E U) n=p+1 dengan A := AI. Pertimbangkan dua fungsi dalam Ap. Hasil darab Hadamard (atau konvolusi) untuk 1 dan 9 ialah fungsi 1 * 9 berbentuk 00 (J * g)(z) = zP + L anbnzn. n=p+1 Let C be the complex plane and U := {z E C : Izl < I} be the open unit disk in C and H(U) be the class of analytic functions defined in U. Also let A denote the class of all functions I analytic in the open unit disk U := {z E C : Izl < I}, and normalized by 1(0) = 0, and 1'(0) = 1. A function I E A has the Taylor series expansion of the form 00 I(z) = z + ~ (LnZn (z E U). n=2 Let Ap (p EN) be the class of all analytic functions of the form 00 fez) = zP + ~ (LnZn n=p+l with A:= AI. Consider two functions in Ap. The Hadamard product (or convolution) of I and 9 is the function I * 9 defined by 00 (J * g)(z) = zP + ~ anbnzn . "=p+

On certain classes of univalent meromorphic functions associated with integral operators

This paper illustrates how some inclusion relationships of certain class of univalent meromorphic functions may be defined by using the linear operator. Further, a property preserving integrals is considered for the final outcome of the study.Publisher's Versio