id author title date pages extension mime words sentence flesch summary cache txt cana-1119 Gurmeet Singh Second Hankel Inequality for Certain Common Subclass of Classes of Starlike and Convex Functions 2024 12 .pdf application/pdf 4515 196 57 βˆ’ 2)2(9π‘Ÿ3 βˆ’ 29π‘Ÿ2 + 30π‘Ÿ βˆ’ 12) 576(3 βˆ’ 2π‘Ÿ)2(π‘Ÿ βˆ’ 2)4(3π‘Ÿ βˆ’ 4) From 𝐸′(𝑐) = 0 we will have 𝑐 = 0 𝐸′′(0) = βˆ’ 9π‘Ÿ3 βˆ’ 29π‘Ÿ2 + 30π‘Ÿ βˆ’ 12 24(3 βˆ’ 2π‘Ÿ)2(π‘Ÿ βˆ’ 2)2(3π‘Ÿ βˆ’ 4) that we can easily conclude that 𝐸′′(0) is Negative, which implies that at 𝑐 = 0 the function will attain its maxima. |π‘Ž2π‘Ž4 βˆ’ π‘Ž3 2| ≀ 1 4(3 βˆ’ 2π‘Ÿ)2 Corollary When π‘Ÿ = 0, we have β„Ž ∈ π‘†βˆ—πΆsin (0):= 𝐢sin and we get |π‘Ž2π‘Ž4 βˆ’ π‘Ž3 2| ≀ 1 36 When π‘Ÿ = 1 we have β„Ž ∈ π‘†βˆ—πΆsin(1):= 𝑆sin βˆ— , and we get |π‘Ž2π‘Ž4 βˆ’ π‘Ž3 2| ≀ 1 4 4. From (15), we Have π‘Ž4 = 1 288(π‘Ÿ βˆ’ 2)3(6π‘Ÿ2 βˆ’ 17π‘Ÿ + 12) cache/cana-1119.pdf txt/cana-1119.txt