We establish the subadditivity of strongly operator convex functions on $(0, \\\\\\\\infty)$ and $(-\\\\\\\\infty,0)$. By utilizing the properties of strongly operator convex functions, we derive the subadditivity property of operator monotone functions on $(-\\\\\\\\infty,0)$. 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 $(0, \\\\\\\\infty)$. Moreover, we study strongly operator convex functions on $(a, \\\\\\\\infty)$ with $-\\\\\\\\infty0$.

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