Generalized conditions for starlikeness and convexity of certain analytic functions

Close-to-convexity, starlikeness, and convexity of certain analytic functions

‘The present investigation was supported, in part, by the Japanese Ministry of Education, Science and Culture tinder Grant-in-Aid for General Scientific Research (No. 046204) and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant 0GP0007353. A preliminary report on this paper was presented at the spring meeting of the Mathematical Society of Japan held at W...

CERTAIN SUFFICIENT CONDITIONS FOR CLOSE-TO-CONVEXITY OF ANALYTIC FUNCTIONS

The object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk  

On starlikeness and close-to-convexity of certain analytic functions

Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

For α ≥ 0, λ > 0, we consider theM α, λ b of normalized analytic α−λ convex functions defined in the open unit disc U. In this paper, we investigate the classM α, λ b, that is, Re{ zf ′ b z /fb z 1− α α 1 − λ zf ′ b z /fb z αλ 1 zf ′′ b z /f ′ b z } > 0, with fb is Koebe type, that is, fb z : z/ 1−zn . The subordination result for the aforementioned class will be given. Further, bymaking use of...

certain sufficient conditions for close-to-convexity of analytic functions

the object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk