‎In this paper‎, ‎we present several sharp upper bounds for the numerical radii of the diagonal and off-diagonal parts of‎ ‎the $ 2 \\\\times 2$ block operator matrix‎ ‎$ \\\\begin{bmatrix}‎ ‎A& B \\\\\\\\‎ ‎C& D \\\\end{bmatrix} $‎. ‎Among extensions of some results of Kittaneh et al.‎, ‎it is shown that if‎ ‎$ T= \\\\begin{bmatrix}‎ ‎A& 0 \\\\\\\\‎ ‎0& D \\\\end{bmatrix}$‎, ‎and $f$ and $g$ are non-negative continuous functions on $ [0‎, ‎\\\\infty ) $ such that $ f(t)g(t)=t \\\\ (t \\\\geq 0) $‎, ‎then for all non-negative nondecreasing convex functions $h$ on‎ ‎$ [0‎, ‎\\\\infty ) $‎, ‎we obtain that‎ ‎\\\\begin{align*}‎ ‎& h\\\\left( w^r(T)\\\\right) \\\\\\\\‎ ‎& \\\\leq \\\\max \\\\left(‎ ‎\\\\left\\\\| \\\\frac{1}{p} h\\\\left(f^{pr}(\\\\left| A \\\\right| )\\\\right)‎+ ‎\\\\frac{1}{q}h\\\\left(g^{qr}(\\\\left| A^* \\\\right| )\\\\right)\\\\right\\\\|‎ ,‎\\\\left\\\\|\\\\frac{1}{p} h\\\\left( f^{pr}(\\\\left| D \\\\right| )\\\\right)‎+ ‎\\\\frac{1}{q}h\\\\left(g^{qr}(\\\\left| D^* \\\\right| )\\\\right)\\\\right\\\\|\\\\right)‎, ‎\\\\end{align*}‎ ‎where $ p‎, ‎q > 1 $ with‎ ‎$\\\\frac{1}{p}‎ + ‎\\\\frac{1}{q} =1$‎, ‎and $ r \\\\min (p‎, ‎q )\\\\geq 2 $‎.

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