Abstract:In this paper we give extensions of Sherman’s inequality considering the class of convex functions of higher order. As particular cases, we get an extended weighted majorization inequality as well as Jensen’s inequality which have direct connection to information theory. We use the obtained results to derive new estimates for Shannon’s and Rényi’s entropy, information energy, and some well-known measures between probability distributions. Using the Zipf–Mandelbrot law, we introduce new functionals to derive so… Show more
“…In this section, we give some interesting estimates for the integral Csiszár divergence and for its important particular cases (see, e.g., [4,5,9,10,12,15]). , and let a 0 , a 1 , .…”
Section: Applications In Information Theorymentioning
In this paper, we give refinements of the integral form of Jensen's inequality and the Lah-Ribarič inequality. Using these results, we obtain a refinement of the Hölder inequality and a refinement of some inequalities for integral power means and quasiarithmetic means. We also give applications in information theory, namely, we give some interesting estimates for the integral Csiszár divergence and its important particular cases.
MSC: 26D15; 94A15
“…In this section, we give some interesting estimates for the integral Csiszár divergence and for its important particular cases (see, e.g., [4,5,9,10,12,15]). , and let a 0 , a 1 , .…”
Section: Applications In Information Theorymentioning
In this paper, we give refinements of the integral form of Jensen's inequality and the Lah-Ribarič inequality. Using these results, we obtain a refinement of the Hölder inequality and a refinement of some inequalities for integral power means and quasiarithmetic means. We also give applications in information theory, namely, we give some interesting estimates for the integral Csiszár divergence and its important particular cases.
MSC: 26D15; 94A15
“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”
Section: ) We Get Majorization Inequalitymentioning
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n -strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f -divergence and derived some reverse relations for such concept.
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