Common coupled fixed point results for operators without mixed monotone type properties and application to nonlinear integral equations. (English) Zbl 1447.47046
In this paper, in the context of an ordered Banach space, the author proves some common coupled fixed point theorems for a pair of operators without assuming the mixed monotone type property. The main assumptions on the operators are some condensing and contraction type conditions involving the measures of noncompactness of Kuratowski and De Blasi and the condition of being weakly inflationary (or weakly deflationary) for the given pair of operators. As an application, existence and uniqueness results of nonnegative solutions for nonlinear integral equations are given.
Reviewer: Adrian Petruşel (Cluj-Napoca)
MSC:
| 47H10 | Fixed-point theorems |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 45G15 | Systems of nonlinear integral equations |
Keywords:
ordered Banach space; fixed point; coupled fixed point; mixed monotone property; inflationary pair of mappingsReferences:
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