TITLE:
New Fixed Point Theorems of Mixed Monotone Operators
AUTHORS:
Xinsheng Du
KEYWORDS:
Mixed Monotone Operators; Cone; Partial Order
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.3,
February
7,
2014
ABSTRACT: Mixed monotone operator is
an important nonlinear operator. It exists extensively in the research of
nonlinear differential and integral equations. Generally, the research of mixed
monotone operators in partially ordered Banach spaces requires compactness,
continuity or concavity-convexity of the operators. In this paper, without any
compact and continuous assumption, we obtain some new existence and uniqueness
theorems of positive fixed point of e-concave-convex mixed monotone operators
in Banach spaces partially ordered by a cone, which extends the existing
corresponding results.