Uniform Treatment of Jensen’s Inequality by Montgomery Identity

Tahir Rasheed, Saad Ihsan Butt, Ä ilda PeÄ arić, Josip PeÄ arić, Ahmet Ocak Akdemir and Xiaolong Qin

Journal of Mathematics, 2021, vol. 2021, 1-17

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5564647

DOI: 10.1155/2021/5564647

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