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March 3, 2026Journal of Inequalities and Applications1 citationsOpen Access

Matrix Hermite–Hadamard type inequalities for bivariate convex functions

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MKMohsen KianUniversity of BojnordMDM. Rostamian DelavarUniversity of Bojnord

Key Points

  • The study presents significant results regarding the Hermite–Hadamard inequality for bivariate functions and matrices.
  • Results indicate that separately convex bivariate functions lead to majorization and norm inequalities, expanding previous conclusions.
  • Assessment using matrix convexity identifies a set of inequalities relevant to bivariate matrix functions, enhancing understanding in this area.
  • These findings generalize earlier research on the Hermite–Hadamard inequality, indicating broader implications in convex analysis.

Abstract

Considering convexity as well as matrix convexity for bivariate functions, we investigate the well-known Hermite–Hadamard inequality. In the case of separately convex bivariate functions, we present some majorization and norm inequalities. In the case of matrix convexity, a series of matrix inequalities are presented for bivariate matrix functions. Our results generalize some previous studies concerning Hermite–Hadamard inequality.

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Cite This Study

Kian et al. (2026) studied this question.

synapsesocial.com/papers/69a760aac6e9836116a2da0chttps://doi.org/10.1186/s13660-026-03426-7
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