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Volume 6, Issue 5, 1 October 2022, Pages 567-584
Abstract. We consider an elliptic variational-hemivariational inequality in a -uniformly smooth Banach space. We prove that the inequality is governed by a multivalued maximal monotone operator, and, for each , we use the resolvent of this operator to construct an auxiliary fixed point problem, denoted . Next, we perform a parallel study of problems and based on their intrinsic equivalence. In this way, we prove existence, uniqueness, and well-posedness results with respect to specific Tykhonov triples. The existence of a unique common solution to problems and is proved by using the Banach contraction principle in the study of Problem . In contrast, the well-posedness of the problems is obtained by using a monotonicity argument in the study of Problem . Finally, the properties of Problem allow us to deduce a convergence criterion in the study of Problem .
How to Cite this Article:
Rong Hu, Mircea Sofonea, On the well-posedness of variational-hemivariational inequalities and associated fixed point problems, J. Nonlinear Var. Anal. 6 (2022), 567-584.