Surjectivity of -accretive operators

Authors:
Jong An Park and Sehie Park

Journal:
Proc. Amer. Math. Soc. **90** (1984), 289-292

MSC:
Primary 47H15

DOI:
https://doi.org/10.1090/S0002-9939-1984-0727252-3

MathSciNet review:
727252

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Abstract: Let and be Banach spaces, and ; is said to be strongly -accretive if for some and each , . These maps constitute a generalization simultaneously of monotone maps (when ) and accretive maps (when ). By applying the Caristi-Kirk fixed point theorem, W. O. Ray showed that a localized class of these maps must be surjective under appropriate geometric assumptions on and continuity assumptions on the duality map. In this paper we show that such geometric assumptions can be removed without affecting the conclusion of Ray.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0727252-3

Keywords:
Strongly -accretive,
locally strongly -accretive,
strongly upper semicontinuous

Article copyright:
© Copyright 1984
American Mathematical Society