2020/05/07 by Najla M. Alarifi, Alarifi, Najla M.
Mathematics · #30C50 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30C45 #Secondary: 30C80
paper · pdf · doi:10.48550/arxiv.2005.03714
openalex publication_date 2020/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A,B,D,E belong to [-1, 1] and let p(z) be an analytic function with fixed initial coefficient defined in the open unit disk. Conditions on A,B,D,and E are determined so that 1+αzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz) and other similar implications involving 1+αzp'(z)/p(z), αp2(z)+λzp'(z),αp(z)+(1-α)p2(z)+λzp'(z),and (1-α)p(z)+alpha(1+zp'(z)/p(z)). Also, sufficient conditions for Janowski starlikeness with fixed second coefficient are obtained.