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+

Differential Subordination And Coefficients Problems Of Certain Analytic Functions

Let A be the class of normalized analytic functions f on the unit disk D, in the form f(z) = z+ P1n =2 anzn: A function f in A is univalent if it is a one-to-one mapping. This thesis discussed ¯ve research problems. Lambangkan A sebagai kelas fungsi analisis ternormal pada cakera unit D berbentuk f(z) = z + P1n =2 anzn: Fungsi f dalam A adalah univalen jika fungsi tersebut ialah pemetaan satu ke satu. Tesis ini mengkaji lima masalah penye- lidikan

Convolution and coefficient problems for multivalent functions defined by subordination [QA1].

Dalam Bab 1, kelas-kelas teritlak bak-bintang multivalen, cembung, hampir-cembung dan kuasi-cembung diperkenalkan. Kelas-kelas tersebut memberi kaedah penyatuan untuk pelbagai subkelas yang diketahui sebelum ini. In Chapter 1, the general classes of multi-valent starlike, convex, close-to-convex and quasi-convex functions are introduced. These classes provide a unified treatment to various known subclasses

Bounds for the Second Hankel Determinant of Certain Univalent Functions

The estimates for the second Hankel determinant a_2a_4-a_3^2 of analytic function f(z)=z+a_2 z^2+a_3 z^3+...b for which either zf'(z)/f(z) or 1+zf"(z)/f'(z) is subordinate to certain analytic function are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike, lemniscate starlike functions are obtained

Initial Coefficients of Biunivalent Functions

An analytic function f defined on the open unit disk is biunivalent if the function f and its inverse f-1 are univalent in . Estimates for the initial coefficients of biunivalent functions f are investigated when f and f-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results

Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made