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A novel proof of the existence of solutions for a new system of generalized mixed quasi-variational-like inclusions involving (A, η, m)-accretive operators

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Abstract

In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with (A, η, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prove the existence of solutions for this general system of generalized mixed quasi-variational-like inclusions and its special cases. The results in this paper unify, extend and improve some known results in the literature. The novel proof method is simpler than those iterative algorithm approach for proving the existence of solutions of all classes of system of set-valued variational inclusions in the literature.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, P.R. China

    Jian-Wen Peng

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  1. Jian-Wen Peng
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Peng, JW. A novel proof of the existence of solutions for a new system of generalized mixed quasi-variational-like inclusions involving (A, η, m)-accretive operators. J Glob Optim 42, 559–575 (2008). https://doi.org/10.1007/s10898-008-9278-x

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  • DOI: https://doi.org/10.1007/s10898-008-9278-x

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