Displaying similar documents to “Perturbations of normally solvable nonlinear operators. I.”

On some nonlinear alternatives of Leray-Schauder type and functional integral equations

Bapurao Chandra Dhage (2006)

Archivum Mathematicum

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In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl....

Sets in the ranges of nonlinear accretive operators in Banach spaces

Athanassios Kartsatos (1995)

Studia Mathematica

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Let X be a real Banach space and G ⊂ X open and bounded. Assume that one of the following conditions is satisfied: (i) X* is uniformly convex and T:Ḡ→ X is demicontinuous and accretive; (ii) T:Ḡ→ X is continuous and accretive; (iii) T:X ⊃ D(T)→ X is m-accretive and Ḡ ⊂ D(T). Assume, further, that M ⊂ X is pathwise connected and such that M ∩ TG ≠ ∅ and M ∩ T ( ∂ G ) ¯ = ∅ . Then M ⊂ T G ¯ . If, moreover, Case (i) or (ii) holds and T is of type ( S 1 ) , or Case (iii) holds and T is of type ( S 2 ) , then M ⊂ TG. Various results...