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.


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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