We consider an inclusion problem governed by a strongly monotone
Lipschitz continuous operator defined on a real Hilbert space. We
list the assumption on the data and recall the existence of a
unique solution to the problem. Then we introduce several Tykhonov
triples, compare them and prove the corresponding well-posedness
results. Moreover, using the approximating sequences generated by
these triples, we obtain various convergence results. In particular,
with a specific choice of the Tykhonov triple, we deduce a criterion
of convergence to the solution of the inclusion. The proofs of our
results are based on arguments of compactness, pseudomonotonicity,
convexity, fixed point and the Mosco convergence of sets.
Key Words: Normal cone, monotone operator,
inclusion, Tykhonov triple, Tykhonov well-posedness, approximating
sequence, fixed point, Mosco convergence.
2010 Mathematics Subject Classification: Primary
47J22; Secondary 49J40, 49J21, 34G25.
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