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In this paper, we present some unitarily invariant norm inequalities for sector matrices involving a special class of functions. In particular, if  is a $2n\times 2n$ matrix such that numerical range of Z is contained in a sector region $S_{\alpha } $ for some $\alpha \in [0,\frac{\pi }{2} ) $, then, for a submultiplicative function h of the class $\mathcal{C} $ and every unitarily invariant norm, we have $$\begin{aligned} \bigl\Vert h \bigl( \vert Z_{ij} \vert ^{2} \bigr) \bigr\Vert &\leq \bigl\Vert h^{r} \bigl( \sec (\alpha ) \vert Z_{11} \vert \bigr) \bigr\Vert ^{\frac{1}{r} } \bigl\Vert h^{s} \bigl( \sec (\alpha ) \vert Z_{22} \vert \bigr) \bigr\Vert ^{ \frac{1}{s} }, \end{aligned}$$  where r and s are positive real numbers with $\frac{1}{r}+\frac{1}{s}=1 $ and $i,j=1,2$. We also extend some unitarily invariant norm inequalities for sector matrices.

Norm inequalities involving a special class of functions for sector matrices