PENCIRIAN FUNGSI BAK-BINTANG PARABOLIK DAN FUNGSI CEMBUNG SECARA SERAGAM TERITLAK
| dc.contributor.author | KEONG, LEE SEE | |
| dc.date.accessioned | 2016-01-12T03:54:15Z | |
| dc.date.available | 2016-01-12T03:54:15Z | |
| dc.date.issued | 2000-03 | |
| dc.description.abstract | Let U = { z : I z I < 1 } be the open unit disk in the complex plane and S be the class of analytic = univalent functions f(z) = z + L, anzn normalized so that f(O) = f' (0) -1 = 0. Let C n=2 denote the class of functions g E S which maps U onto a convex domain. Also, let s* denote the class of functions f E S which maps U onto a domain starlike with respect to the origin. A. W. Goodman introduced the class of uniformly convex functions CSS consisting of functions g E C with the property that for every circular arc r contained in U, with center also in U, the image arc g(y) is a convex arc. Similarly, Goodman defined the class of uniformly starlike functions BBS consisting of functions f E S • with the property that for every circular arc r contained in U, with center also in U, the image arc j(y) is a starlike arc with respect to the origin. For the classes C and s*, it is known that g E C if and only if f = zg' E S *. One would expect then that there would be a similar relation between CSS and BBS. However, this is not true as proved by Goodman, in which he showed that a function f = zg' E BBS does not necessarily imply that g E CSS . For functions f E BBS which actually satisfy the above condition, F. RlZ\nning categorized these functions to be in the class S P, that is f = zg' E S P if and only if g E CSS. Geometrically, the function f E S P will map U into a parabolic region Q = { w = u + iv : v 2 < 2u - 1 } = { w: I w - 1 I< Ny w } IX R. M. Ali and V. Singh generalized the class S P by allowing the above parabolic region n to vary so that the vertex will be located within the interval (0,1) on the real axis. In this thesis, we will generalize the class CSS to a class CSS(p) and relate it with the generalized class Sp(p). Some analytic properties of the generalized CSS(p) will be obtained. We will also obtain the sharp bound for the Fekete- Szego functional I a 3 - pa/ I ~ for functions j(z) = Z + L anzn E S p (p). n=2 Finally, we will study the generalized hypergeometric functions and determine conditions for these functions to be in the class CSS(p) and S P (p). | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/1499 | |
| dc.subject | PENCIRIAN FUNGSI BAK-BINTANG PARABOLIK | en_US |
| dc.title | PENCIRIAN FUNGSI BAK-BINTANG PARABOLIK DAN FUNGSI CEMBUNG SECARA SERAGAM TERITLAK | en_US |
| dc.type | Thesis | en_US |
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