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Measures of noncompactness and infinite systems of integral equations of Urysohn type in \(L^\infty (\mathfrak{G})\). (English) Zbl 1485.47076

Summary: In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space \(L^\infty(\mathfrak{G})\) (where \(\mathfrak{G}\subseteq\mathbb{R}^\omega)\) are proved. We handle our obtained consequences to inquire the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example.

MSC:

47H10 Fixed-point theorems
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
45G15 Systems of nonlinear integral equations
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