Over the (1, N)-dimensional real superspace, N = 2,3, we classify osp(N|2)-invariant binary differential operators acting on the superspaces of weighted densities, where osp(N|2) is the orthosymplectic Lie superalgebra. This result allows us to compute the first differential osp(N|2)-relative cohomology of the Lie superalgebra κ(N) of contact vector fields with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities. We classify generic formal osp(32)-trivial deformations of the κ(3)-module structure on the superspaces of symbols of differential operators. We prove that any generic formal osp(3|2)-trivial deformation of this κ(3)-module is equivalent to its infinitesimal part. This work is the simplest generalization of a result by the first author et al. [Basdouri, I., Ben Ammar, M., Ben Fraj, N., Boujelbene, M., and Kammoun, K., "Cohomology of the Lie superalgebra of contact vector fields on K~(1|1) and deformations of the superspace of symbols," J. Nonlinear Math. Phys.16, 373 (2009)10.1142/S1402925109000431].
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