Around strongly operator convex functions

Abstract

We establish the subadditivity of strongly operator convex functions on (0,∞) and (−∞,0). By utilizing the properties of strongly operator convex functions, we derive the subadditivity property of operator monotone functions on (−∞,0). We introduce new operator inequalities involving strongly operator convex functions and weighted operator means. In addition, we explore the relationship between strongly operator convex and Kwong functions on (0,∞). Moreover, we study strongly operator convex functions on (a,∞) with −∞<a and on the left half-line (−∞,b) with b<∞. We demonstrate that any nonconstant strongly operator convex function on (a,∞) is strictly operator decreasing, and any nonconstant strongly operator convex function on (−∞,b) is strictly operator monotone. Consequently, for a strongly operator convex function g on (a,∞) or (−∞,b), we provide lower bounds for |g(A)−g(B)| whenever A−B>0.