Around strongly operator convex functions

We establish the subadditivity of strongly operator convex functions on (0,infinity) and (-infinity,0). By utilizing the properties of strongly operator convex functions, we derive the subadditivity property of operator monotone functions on (-infinity,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,infinity). Moreover, we study strongly operator convex functions on (a,infinity) with -infinity<a and on the left half-line (-infinity,b) with b<infinity. We demonstrate that any nonconstant strongly operator convex function on (a,infinity) is strictly operator decreasing, and any nonconstant strongly operator convex function on (-infinity,b) is strictly operator monotone. Consequently, for a strongly operator convex function g on (a,infinity) or (-infinity,b), we provide lower bounds for |g(A)-g(B)| whenever A-B>0. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.