# On the Maximality of Sums of Nonlinear Monotone Operators

@inproceedings{Rockafellar2010OnTM, title={On the Maximality of Sums of Nonlinear Monotone Operators}, author={R. Tyrrell Rockafellar}, year={2010} }

- Published 2010

is called the effective domain of F, and F is said to be locally bounded at a point x e D(T) if there exists a neighborhood U of x such that the set (1.4) T(U) = (J{T(u)\ueU} is a bounded subset of X. It is apparent that, given any two monotone operators Tx and T2 from X to X*, the operator F», + T2 is again monotone, where (1 5) (Ti + T2)(x) = Tx(x) + T2(x) = {*? +x% I xf e Tx(x), xt e T2(x)}. If Tx and F2 are maximal, it does not necessarily follow, however, that F», + T2 is maximal—some sort… CONTINUE READING

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#### References

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