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An integral inequality

open access: yesJournal of Mathematical Analysis and Applications, 1981
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An integral inequality

open access: yesDuke Mathematical Journal, 1943
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Integral and discrete inequalities

open access: yesJournal of Numerical Analysis and Approximation Theory, 1992
Some discrete analogues of known integral inequalities are proved. For example, the following discrete version of Fejér's generalization of Hadamard's inequalities is valid: If the sequence \((x_ i)^ n_{i=1}\) is convex and \((p_ i)^ n_{i=1}\) is symmetric, i.e., \(p_ i=p_{n-i+1}\) for \(i=1,\dots,n\), and positive, then: \[ \biggl(x_{[(n+1)/2]}+x_{[(n+
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