All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 1147

Showing per page

A class of analytic functions defined by Ruscheweyh derivative

K. S. Padmanabhan, M. Jayamala (1991)

Annales Polonici Mathematici

The function f ( z ) = z p + ∑ k = 1 ∞ a p + k z p + k (p ∈ ℕ = 1,2,3,...) analytic in the unit disk E is said to be in the class K n , p ( h ) if ( D n + p f ) / ( D n + p - 1 f ) ≺ h , where D n + p - 1 f = ( z p ) / ( ( 1 - z ) p + n ) * f and h is convex univalent in E with h(0) = 1. We study the class K n , p ( h ) and investigate whether the inclusion relation K n + 1 , p ( h ) ⊆ K n , p ( h ) holds for p > 1. Some coefficient estimates for the class are also obtained. The class A n , p ( a , h ) of functions satisfying the condition a * ( D n + p f ) / ( D n + p - 1 f ) + ( 1 - a ) * ( D n + p + 1 f ) / ( D n + p f ) ≺ h is also studied.

Currently displaying 1 – 20 of 1147

Page 1 Next