Abstract
The aim of this paper is to establish existence and boundedness theorems for perturbed variational inequalities defined by a set-valued mapping without any kind of monotonicity in Banach spaces. The first result is shown that if a coercivity condition holds, then the solution set of a variational inequality perturbed along a direction is nonempty and uniformly bounded. Second, by employing the Minty variational inequalities perturbed by a nonlinear mapping without monotonicity, we prove the boundedness result for the corresponding perturbed variational inequalities under a kind of coercivity condition.
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Wang, M. Existence theorems for perturbed variational inequalities in Banach spaces. J. Fixed Point Theory Appl. 20, 55 (2018). https://doi.org/10.1007/s11784-018-0536-3
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DOI: https://doi.org/10.1007/s11784-018-0536-3
Keywords
- Perturbed variational inequalities
- Minty perturbed variational inequalities
- Coercivity conditions
- Upper semicontinuous