2021/01/15 by Kanika Sharma, Sharma, Kanika, Rasoul Aghalary +3
Mathematics · Physics and Astronomy · #30C45 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Waves and Solitons #math.CV #msc:30C45 #msc:30C80
paper · pdf · doi:10.48550/arxiv.2101.06041
arxiv created 2021/01/15 · openalex publication_date 2021/01/15 · arxiv updated 2021/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The conditions on A, B, β and γ are obtained for an analytic function p defined on the open unit disc \mathbbD and normalized by p(0)=1 to be subordinate to (1+Az)/(1+Bz), -1≤ B<A ≤ 1 when p(z)+ zp'(z)/(βp(z)+γ) is subordinate to ez. The conditions on these parameters are derived for the function p to be subordinate to √(1+z) or ez when p(z)+ zp'(z)/(βp(z)+γ) is subordinate to (1+Az)/(1+Bz). The conditions on β and γ are determined for the function p to be subordinate to ez when p(z)+ zp'(z)/(βp(z)+γ) is subordinate to √(1+z). Related result for the function p(z)+ zp'(z)/(βp(z)+γ) to be in the parabolic region bounded by the Re w=|w-1| is investigated. Sufficient conditions for the Bernardi's integral operator to belong to the various subclasses of starlike functions are obtained as applications