Abstract: In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.

Key words: quadratic minimization, generalized equilibrium, fixed point, variational inclusion, multi-valued maximal monotone mapping, inverse-strongly monotone mapping, resolvent operator, nonexpansive mapping