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Zeitschrift für Analysis und ihre Anwendungen

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Volume 23, Issue 2, 2004, pp. 293–302
DOI: 10.4171/ZAA/1199

Published online: 2004-06-30

F-Implicit Complementarity Problems in Banach Spaces

Nan-jing Huang[1] and Jun Li[2]

(1) Sichuan University, China
(2) China West Normal University, Sichuan, China

The F-implicit complementarity problem (F-ICP) and F-implicit variational inequality problem (F-IVIP) are introduced and studied. The equivalence between (F-ICP) and (F-IVIP) is presented under certain assumptions. Furthermore, we derive some new existence theorems of solutions for (F-ICP) and (F-IVIP) by using the Fan-Knaster-Kuratowski-Mazurkiewicz Math. Ann. 142 (1961), 305 -- 310] and Lin's Bull. Austral. Math. Soc. 34 (1986), 107 -- 117] under some suitable assumptions without the monotonicity.

Keywords: F-implicit complimentarity problem, F-implicit variational inequality, equivalence, Knaster-Kuratowski-Mazurkiewicz-mapping

Huang Nan-jing, Li Jun: F-Implicit Complementarity Problems in Banach Spaces. Z. Anal. Anwend. 23 (2004), 293-302. doi: 10.4171/ZAA/1199