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On Some Generalization of Inequalities of Opial, Yang and Shum

Published online by Cambridge University Press:  20 November 2018

Cheng-Shyong Lee
Cheng-Shyong Lee*
Affiliation:
Department of Mathematics, Evening School, Tamkang College of Arts and Science 5, Lane 199, King-Hwa street, Taipei, Taiwan (106), Republic of China
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In 1960, Z. Opial [20] proved the following interesting integral inequality:

Theorem A. If u is a continuously differentiable function on [0, b], and if u(0) = u(b) = 0, and u(x)>0 for x∊(0, b), then

1

where the constant b/4 is the best possible.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 71 - 80
Copyright
Copyright © Canadian Mathematical Society 1980

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