APPLICATIONS OF CERTAIN FUNCTIONS ASSOCIATED WITH LEMNISCATE BERNOULLI
Abstract: For J(α; f(z)) = (1
− α) zf f( ′z (z )) + α [1 + zf f ′ ′′ (z (z )) ] (α ≥ 0), denote SL(α) and SLc
as classes of α-convex and convex functions which respectively satisfy conditions
| [J(α; f(z))]2 − 1| < 1 and [1 + zf f ′ ′′ (z (z )) ]2 − 1 < 1. Using
established results, namely 1 + βzp′(z) ≺ 1+ 1+Dz Ez
; 1 + βzp p(′z()z) ≺ 1+ 1+Dz Ez
and 1 + βzp p2( ′z (z )) ≺ 1+ 1+Dz Ez
imply p(z) ≺ √1 + z where p(z) is an analytic
function defined on the open unitdisk D with p(0) = 1. This article
obtains conditions so that analytic functions f belong to the classes SL(α) and
SLc.
Author: Suzeini Abdul Halim
and Rashidah Omar
Journal Code: jpmatematikagg120017
