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Mathematical Notes of the Academy of Sciences of the USSR, 1969
The author proves the following analogue to a well-known result of Hardy and Littlewood [\textit{G. H. Hardy, J. E. Littlewood} and \textit{G. Pólya} [Inequalities. 2nd ed. Cambridge: At the University Press (1952; Zbl 0047.05302), Theorem 382]. Let \(p, q, r, s, t\) be positive numbers such that \(q>1\), \(1/p+1/q>1\), and either (i) \(11\). If \(u=(2-
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The author proves the following analogue to a well-known result of Hardy and Littlewood [\textit{G. H. Hardy, J. E. Littlewood} and \textit{G. Pólya} [Inequalities. 2nd ed. Cambridge: At the University Press (1952; Zbl 0047.05302), Theorem 382]. Let \(p, q, r, s, t\) be positive numbers such that \(q>1\), \(1/p+1/q>1\), and either (i) \(11\). If \(u=(2-
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On a Class of Integral Inequalities
Journal of the London Mathematical Society, 1978Everitt, W. N., Zettl, A.
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2000
Some integral inequalities of the following type are proved: Suppose \(f\) has a continuous \(n\)th order derivative on \([a,b]\); \(f^{(i)}(a)\geq 0\) and \(f^{(n)}(x)\geq n!\) for all \(x\in [a,b]\) and \(0\leq i\leq n-1\). Then \[ \int^b_a [f(x)]^{n+2} dx\geq \Biggl[\int^b_a f(x) dx\Biggr]^{n+ 1}. \] An open problem is also stated.
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Some integral inequalities of the following type are proved: Suppose \(f\) has a continuous \(n\)th order derivative on \([a,b]\); \(f^{(i)}(a)\geq 0\) and \(f^{(n)}(x)\geq n!\) for all \(x\in [a,b]\) and \(0\leq i\leq n-1\). Then \[ \int^b_a [f(x)]^{n+2} dx\geq \Biggl[\int^b_a f(x) dx\Biggr]^{n+ 1}. \] An open problem is also stated.
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Further Integral Inequalities through Some Generalized Fractional Integral Operators
Fractal and Fractional, 2021Abd-Allah Hyder +2 more
exaly
New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators
Mathematics, 2021Maria Alessandra Ragusa +2 more
exaly
INEQUALITIES FOR INTEGRAL FUNCTIONS
The Quarterly Journal of Mathematics, 1958openaire +2 more sources
On the Ostrowski type integral inequality
2010Motivated by Ostrowski's inequality and some related investigations, the author presents an inequality for functions \(f:[a,b]\times [c,d]\to \mathbb R\) fulfilling further regularity properties.
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