Mixed monotone operators and their application to integral equations. (English) Zbl 1453.47010
Summary: In this paper, we investigate the mixed monotone operators of a new type in a Cartesian product of a Banach space with an order determined by a normal cone. We establish sufficient conditions for such operators to have a unique fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. We also apply the obtained results to prove the existence and uniqueness of a solution of a nonlinear integral equation.
MSC:
| 47H10 | Fixed-point theorems |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
| 45G05 | Singular nonlinear integral equations |
Keywords:
\((e,u)\)-concave-convex operator; fixed point; mixed monotone operator; nonlinear integral equation; existence; uniquenessReferences:
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