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Zeitschrift für Analysis und ihre Anwendungen

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Volume 22, Issue 3, 2003, pp. 529–542
DOI: 10.4171/ZAA/1160

Published online: 2003-09-30

Fixed Point Theorems for a Class of Mixed Monotone Operators

Zhandong Liang[1], Lingling Zhang[2] and Shengjia Li[3]

(1) ShanXi University, Taiyuan, China
(2) Taiyuan University of Technology, China
(3) ShanXi University, Taiyuan, China

We study a class of mixed monotone operators with convexity and concavity. In particular, we give conditions, both necessary and sufficient, for the existence and uniqueness of fixed points. Moreover, we sketch a simple application of our main theorem and generalize some previous results.

Keywords: Banach space, cone, mixed monotone operator, fixed point

Liang Zhandong, Zhang Lingling, Li Shengjia: Fixed Point Theorems for a Class of Mixed Monotone Operators. Z. Anal. Anwend. 22 (2003), 529-542. doi: 10.4171/ZAA/1160