On extensions of some theorems of Flett. II
Copyright policy )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 \(\limsup_{y\to \infty} (\gamma(Cy)/\gamma(y)) 1\), then \[ \int^ \pi_{- \pi} h^ \lambda_{k, \alpha,\gamma(t)} (Q) dQ\leq B \int^ \pi_{-\pi} g^ \lambda_{k,\gamma(t)} (Q) dQ. \] {}.
Cesàro, Euler, Nörlund and Hausdorff methods, Inequalities for sums, series and integrals, integral inequalities, Absolute and strong summability, absolute Cesàro summability
Cesàro, Euler, Nörlund and Hausdorff methods, Inequalities for sums, series and integrals, integral inequalities, Absolute and strong summability, absolute Cesàro summability
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