Fixed point theorems for a class of positive mixed monotone operators (Q2883884)
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scientific article; zbMATH DE number 6034381
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed point theorems for a class of positive mixed monotone operators |
scientific article; zbMATH DE number 6034381 |
Statements
Fixed point theorems for a class of positive mixed monotone operators (English)
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14 May 2012
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fixed point theorem
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cone
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Thompson's metric
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mixed monotone operator
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singular boundary-value problem
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positive solution
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The author studies fixed-point theorems for a class of mixed monotone operators. Using Thompson's metric techniques and iterative methods, he constructs monotone sequences which converge to the unique fixed point of the operator. The results extend previous works of \textit{D.-J. Guo} [Appl. Anal. 31, No. 3, 215--224 (1988; Zbl 0688.47019)] and \textit{M.-J. Huang}, \textit{C.-Y. Huang} and \textit{T.-M. Tsai} [Math. Z. 257, No. 3, 581--595 (2007; Zbl 1135.47050)]. Applications to nonlinear second/fourth order boundary-value problems are also considered.
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