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Volume 6, Issue 4, 1 August 2022, Pages 407-420
Abstract. In this paper, we aim to investigate a class of new order-theoretic properties for the resolvent operators, which are called order-preservation properties. As applications, we use these order-preservation properties and several order-theoretic fixed point theorems to prove the existence of extremal solutions for several kinds of variational inequalities arising in mechanics and economics. In contrast to many previous studies, the approaches used in this paper are mainly based on the partial order structure of the underlying spaces, and the obtained results weaken the continuity and monotonicity of the associated mappings.
How to Cite this Article:
Yuehu Wang, Ching-Feng Wen, Jen-Chih Yao, Congjun Zhang, Order-preservation properties of resolvent operators and their applications to variational inequalities, J. Nonlinear Var. Anal. 6 (2022), 407-420.