Matrix Hermite–Hadamard type inequalities for bivariate convex functions

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.

Matrix Hermite–Hadamard type inequalities for bivariate convex functions

Key Points

Abstract

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