Uniform Treatment of Jensen’s Inequality by Montgomery Identity
Keyword(s):
We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n − convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite–Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in q − calculus and fractional integrals. Also, we give applications in information theory for our obtained results, especially for Zipf and Hybrid Zipf–Mandelbrot entropies.
1977 ◽
Vol 20
(3)
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pp. 307-312
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2010 ◽
Vol 82
(1)
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pp. 44-61
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2013 ◽
Vol 87
(2)
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pp. 177-194
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2015 ◽
Vol 268
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pp. 121-128
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2011 ◽
Vol 54
(9-10)
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pp. 2451-2459
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2009 ◽
Vol 85
(99)
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pp. 107-110
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Keyword(s):