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arXiv · 2102.07335

Matrix Fej\'{e}r and Levin-Ste\v{c}kin Inequalities

Mohammad Sababheh·Shiva Sheybani·Hamid Reza Moradi
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Abstract

Fe{j}\'er and Levin-Ste\v{c}kin inequalities treat integrals of the product of convex functions with symmetric functions. The main goal of this article is to present possible matrix versions of these inequalities. In particular, majorization results are shown of Fej\'{e}r type for both convex and log-convex functions. For matrix Levin-Ste\v{c}kin type, we present more rigorous results involving the partial Loewner ordering for Hermitian matrices.

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Mohammad Sababheh, Shiva Sheybani, Hamid Reza Moradi. 2021-02-15. Matrix Fej\'{e}r and Levin-Ste\v{c}kin Inequalities. https://arxiv.org/abs/2102.07335

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