Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Toka Diagana

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

tdiagana@howard.edu

Keywords

  • Algebraic sum
  • sum form
  • variational sum
  • Kato's condition
  • maximal monotone operators

Mathematics Subject Classification

47B44, 47H05; 47A07, 11E05

Suggested citation

T. Diagana. “Variational Sum and Kato's Conjecture.” Journal of Convex Analysis 9 (2002), No. 1, 291–294.

Copyright Heldermann Verlag 2002