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Construction of compact-integral operators on \(BC(\Omega)\) with application to the solvability of functional integral equations. (English) Zbl 1330.47094

Summary: In this article, using the concept of measure of noncompactness, we give some results concerning the compactness and continuity of the nonlinear Volterra and Fredholm integral operators on the space \( BC(\Omega)\) (\(\Omega\) is an unbounded subset of the Euclidean space \(\mathbb{R}^n\)). Then, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results generalize and improve some previous works. We will also include some examples which show that our results are applicable where the previous ones are not.

MSC:

47N20 Applications of operator theory to differential and integral equations
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
45P05 Integral operators
45G10 Other nonlinear integral equations
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Full Text: Euclid