New fixed point theorems for countably condensing maps with an application to functional integral inclusions. (English) Zbl 1493.47065
Summary: This paper presents new fixed point theorems for \(2\times 2\) block operator matrix with countably condensing or countably \(\mathcal{D}\)-set-contraction multi-valued inputs. Our theory will then be used to establish some new existence theorems for coupled system of functional differential inclusions in general Banach spaces under weak topology. Our results generalize, improve and complement a number of earlier works.
MSC:
| 47H10 | Fixed-point theorems |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 47J22 | Variational and other types of inclusions |
Keywords:
countably condensing multimap; functional-integral inclusions; Banach spaces; measure of weak noncompactness; fixed point theoremsReferences:
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