On extensions of some theorems of Flett. II
The present paper is a continuation of \textit{L. Leindler} [Acta Math. Hung. 64, No. 3, 269-283 (1994; Zbl 0805.40006)]and extends some integral inequalities of \textit{T. M. Flett} [Proc. Lond. Math. Soc., III. Ser. 8, 357-387 (1958; Zbl 0109.045)]. A typical result is the following: If \(\lambda\geq k\geq 1\), \(\alpha> \max(1/k, -1/k)\), \(\alpha_ k:= \alpha+ \min(1/k, -1/k)\), and \(\limsup_{y\to \infty} (\gamma(Cy)/\gamma(y))< C^{\alpha_ k}\) holds for some \(C> 1\), then \[ \int^ \pi_{- \pi} h^ \lambda_{k, \alpha,\gamma(t)} (Q) dQ\leq B \int^ \pi_{-\pi} g^ \lambda_{k,\gamma(t)} (Q) dQ. \] {}.
scientific article; zbMATH DE number 638213