Sharpening celebrated convex inequalities with applications to operators and entropies.

The Jensen, Jensen–Mercer, and Hermite–Hadamard inequalities have been key in advancing convex inequalities for scalars and operators, with several applications in fields like mathematical physics, operator theory and mathematical inequalities. This paper presents a new argument leading to interesting refinements of these celebrated inequalities. Applications that include entropy and operator inequalities will be presented. [ABSTRACT FROM AUTHOR]