Abstract:
Conditions are obtained for the image of a given set under a general completely continuous nonlinear integral operator to have convex closure. These results are used to establish the uniqueness of quasi-solutions of nonlinear integral equations of the first kind and to prove the solvability of equations of the first kind on a dense subset of the right-hand sides.
Bibliography: 11 titles.
Keywords:nonlinear integral operator, image of a set, closure, convexity, equation of the first kind.
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