Solving existence problems via \(F\)-contractions. (English) Zbl 1529.47099
Summary: The main results of the paper concern the existence of fixed points of nonlinear \( F\)-contraction and the sum of this type of mapping with a compact operator. The results of Krasnosel’skii type are obtained with a usage of the Hausdorff measure of noncompactness and condensing mappings. The presented new tools give the possibility to verify the existence problems of the solutions for some classes of integral equations.
MSC:
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
fixed point; nonlinear \(F\)-contraction; compact operator; condensing mapping; integral equationReferences:
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