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A new class $\mathcal{R}_n(A,B,\lambda)$ of meromorphically multivalent functions defined by the second-order differential subordination is introduced. Several geometric properties of this new class are studied. The sharp upper bound on $|z|=r<1$ for the functional $\mathrm{Re}\{(\lambda-1)z^{p+1}f'(z)+\frac{\lambda}{p+1}z^{p+2}f''(z)\}$ over the class $\mathcal{R}_n(A,B,0)$ is obtained.