D. J. Guo and V. Lakskmikantham, “Coupled Fixed Points of Mixed Monotone Operator with Applications,” Nonlinear Analysis, Vol. 11, No. 5, 1987, pp. 623-632.

has been cited by the following article:

• 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.