Ranges of perturbed maximal monotone and -accretive operators in Banach spaces

Authors:
Zhengyuan Guan and Athanassios G. Kartsatos

Journal:
Trans. Amer. Math. Soc. **347** (1995), 2403-2435

MSC:
Primary 47H05; Secondary 47H06, 47H11, 47H15

DOI:
https://doi.org/10.1090/S0002-9947-1995-1297527-2

MathSciNet review:
1297527

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Abstract: A more comprehensive and unified theory is developed for the solvability of the inclusions , int , where , and . Here, is a real Banach space and or . Mainly, is either maximal monotone or maccretive, and is either pseudo-monotone or compact. Cases are also considered where has compact resolvents and is continuous and bounded. These results are then used to obtain more concrete sets in the ranges of sums of such operators and . Various results of Browder, Calvert and Gupta, Gupta, Gupta and Hess, and Kartsatos are improved and/or extended. The methods involve the application of a basic result of Browder, concerning pseudo-monotone perturbation of maximal monotone operators, and the Leray-Schauder degree theory.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1297527-2

Keywords:
Maximal monotone operator,
pseudo-monotone operator,
-accretive operator,
compact perturbation,
compact resolvent,
range of sums

Article copyright:
© Copyright 1995
American Mathematical Society