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.
Jensen inequality, convex function, strongly convex function, majorization, Sherman inequality
BRADANOVIC, SLAVICA IVELIC
"Sherman's inequality and its converse for strongly convex functions withapplications to generalizedf-divergences,"
Turkish Journal of Mathematics: Vol. 43:
6, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss6/2