The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions

UDC 517.5 We study an upper bound and the sharp bound of the third-order Hankel determinant for some subfamilies of analytic functions for the parameters α ∈ ( 1,4 / 3 ] and α = 3 / 2 , respectively, also proving the recent conjecture for the sharp bounds made in [Virendra Kumar, Sushil Kumar, V. Ravichandran, Third Hankel determinant for certain classes of analytic functions, Mathematical Analysis I: Approximation Theory, February (2020); DOI: 10.1007/978-981-15-1153-019].