Fixed Point Theorems for Nonlinear Operators with and without Monotonicity in Partially Ordered Banach Spaces
Hui-Sheng Ding, Jin Liang, Ti-Jun Xiao
Fixed Point Theory and Applications · 2010
doi:10.1155/2010/108343 (opens in a new tab)
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Abstract
We establish two fixed point theorems for nonlinear operators on Banach spaces partially ordered by a cone. The first fixed point theorem is concerned with a class of mixed monotone operators. In the second fixed point theorem, the nonlinear operators are neither monotone nor mixed monotone. We also provide an illustrative example for our second result.
Abstract licence: CC BY
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