On univalent functions defined by a generalized Sălăgean operator

By Fatima M. Al-Oboudi. International Journal of Mathematics and Mathematical Sciences, 2004

583 citations recorded by the source corpus.

We introduce a class of univalent functions R n ( λ , α ) defined by a new differential operator D n f ( z ) , n ∈ ℕ 0 = { 0 , 1 , 2 , … } , where D 0 f ( z ) = f ( z ) , D 1 f ( z ) = ( 1 − λ ) f ( z ) + λ z f ′ ( z ) = D λ f ( z ) , λ ≥ 0 , and D n f ( z ) = D λ ( D n − 1 f ( z ) ) . Inclusion relations, extreme points of R n ( λ , α ) , some convolution properties of functions belonging to R n ( λ , α ) , and other results are given.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/317a9f42f44a56714258dfdcc92aaa3981864705

Citations in the corpus

• Inclusion Properties of Certain Subclasses of Analytic Functions (2012, unknown): “• 0),()(,1 ≥=− ββββ zfDzfI nn (See Al-Oboudi [1] ).”