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Existence of solutions for mixed Volterra-Fredholm integral equations. (English) Zbl 1254.45003

Summary: We give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space \(L^{1}[0,\infty)\). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

MSC:

45G10 Other nonlinear integral equations
45B05 Fredholm integral equations
45D05 Volterra integral equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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