On the solutions of some generalization of the Shah-type differential equation

Abstract

∞ k=2f k e sλ k with the exponents 0 < h < λ k ↑ +∞ and the abscissa of absolute convergence σaThe equationγje hjs w = ae hs is considered, where n ≥ 3, h > 0 and a = 0. It is proved that if h n + γ0 > 0 then this equation has a solutionf k e skh , wherefor k ≥ 2 (Lemma 1). For n = 3, a = h 3 + γ0 conditions on parameters γj, under which the function F is pseudostarlike (Theorem 1) or pseudoconvex of order α ∈ [0, h) (Theorem 2) are found.