Positivity 7: 257–265, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Fixed Point Theorems and a New System of
Multivalued Generalized Order Complementarity
NAN-JING HUANG and YA-PING FANG
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P.R. China
Received 9 May 2001; accepted 10 February 2002
Abstract. Some new ﬁxed point and coupled ﬁxed point theorems for multivalued increasing type
mappings are obtained and a new system of multivalued generalized order complementarity problems
is introduced in this paper. In terms of new ﬁxed point and coupled ﬁxed point theorems, we give
some existance results of solutions for this new system of multivalued generalized order comple-
mentarity problems. The results presented in this paper extend and improve the corresponding results
announced by Isac and Kostreva.
Mathematics Subject classiﬁcation (1991): 90C33, 54H25
Key words: Multivated increasing type mapping, ﬁxed point, coupled ﬁxed point, multivalued gen-
eralized order complementarity problem
1. Introduction and preliminaries
It is known that complementarity problem theory is a powerful tool of the current
mathematical technology. Because of the wide applications to mechanics, physics,
optimization and control, nonlinear programming, economics and transportation
equilibrium, and engineering sciences, complementarity problems have been stud-
ied and generalized by many authors for the past years (see [1–6, 8] and the
references therein). In 1991, Isac and Kostreva  introduced a class of general-
ized order complementarity problems and obtained an existence result of solutions
through ﬁxed point theory. In the same year, the generalized order complementarity
problem was extended to multivalued mappings satisfying condition (K) and one
existence result of solutions was obtained by Isac and Kostreva .
Motivated and inspired by [4,5], in this paper, we introduce some concepts
of multivated increasing type mappings and obtain some ﬁxed point and coupled
ﬁxed point theorems for such mappings. We also introduce a new system of multi-
valued generalized order complementarity problems and give some existence res-
This work was supported by the National Natural Science Foundation of China (10171070) and
the Scientiﬁc Research Foundation for the Returned Overseas Chinese Scholars, State Education