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A fixed point theorem for mixed monotone operators with applications. (English) Zbl 0761.47040
The author has investigated the existence of coupled minimal and maximal fixed points for mixed monotone operators. His result includes known theorems about fixed points of increasing and decreasing operators. Some applications to initial value problems and periodic boundary value problems are pointed out.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H05Monotone operators (with respect to duality) and generalizations
Full Text: DOI
[1] Jingxian, Sun; Yong, Sun: Some fixed point theorem of increasing operators. Appl. anal. 23, 23-27 (1986) · Zbl 0585.47046
[2] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S.: Monotone techniques for non-linear differential equations. (1985) · Zbl 0658.35003
[3] Guo, Dajun: Fixed points of mixed monotone operators with applications. Appl. anal. 31, No. No. 3, 215-224 (1988) · Zbl 0688.47019