Mircea Sofonea: Tykhonov triples and convergence analysis of an inclusion problem, 73-96


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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