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Journal of Convex Analysis 09 (2002), No. 1, 291--294
Copyright Heldermann Verlag 2002

Variational Sum and Kato's Conjecture

Toka Diagana
Dept. of Mathematics, Howard University, 2441 6th Street, N.W., Washington, DC 20059, U.S.A.

Our aim in this paper is to compare the variational sum recently introduced by Attouch, Baillon and Théra and the concept of generalized sum. Under appropriate hypotheses, we show that these sums coincide and that the variational sum is a maximal monotone operator.

Keywords: Algebraic sum, sum form, variational sum, Kato's condition, maximal monotone operators.

MSC: 47B44, 47H05; 47A07, 11E05

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