The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination

Fekete-Szegö inequalities associated with k th root transformation based on quasi-subordination

“…Unless otherwise stated, throughout the sequel, we set f is of the form (1) and ϕ, h and w are given by (4), (6) and 5, respectively.…”

“…Inspired by the papers of [1,3,6,7,8], we obtain the upper bounds |b k+1 | and |b 2k+1 | for f ∈ M δ,λ q (γ, ϕ). Also, we investigate the Fekete-Szegö results for the class M δ,λ q (γ, ϕ) and its special cases.…”

Coecients inequalities of kth root transformation for universally prestarlike functions

“…Putting γ = 1 in Corollary (3) we get the result obtained by Gurusamy et. al [3]. By various choices of the function φ and suitably choosing the values of B 1 and B 2 , we state some interesting results analogous to Theorem 2 and the Corollaries 3, 4, 5 and 6.…”

“…Now we determine the Fekete-Szegö inequality |b 2k+1 − µb 2 k+1 | for f ∈ R u α,γ (φ); cf. [5]- [3], [6], [7].…”