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Duality map characterisations for Opial conditions

Published online by Cambridge University Press:  17 April 2009

Tim Dalby  and
Brailey Sims
Tim Dalby
Affiliation:
Department of MathematicsThe University of NewcastleNew South Wales 2308Australia e-mail: [email protected]
Brailey Sims
Affiliation:
Department of MathematicsThe University of NewcastleNew South Wales 2308Australia e-mail: [email protected]
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Abstract

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We characterise Opial's condition, the non-strict Opial condition, and the uniform Opial condition for a Banach space X in terms of properties of the duality mapping from X into X*.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 413 - 417
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Benavides, T. Dominguez, Acedo, G. López and Xu, H–K, ‘Qualitative and quantitative properties for the space ’, (preprint).Google Scholar
[2]Gossez, J.P. and Dozo, E. Lami, ‘Some geometric properties related to the fixed point theory for nonexpansive mappings’, Pacific J. Math. 40 (1972), 565–573.CrossRefGoogle Scholar
[3]Lin, P–K., Tan, K–K. and Xu, H–K., ‘Demiclosedness principle and asymptotic behaviour for asymptotically nonexpansive mappings’, Nonlinear Anal, (to appear).Google Scholar
[4]Opial, Z., ‘Weak convergence of the sequence of successive approximations of nonexpansive mappings’, Bull. Amer. Math. Soc. 73 (1967), 591–597.CrossRefGoogle Scholar
[5]Prus, S., ‘Banach spaces with the uniform Opial property’, Nonlinear Anal. 18 (1992), 697–704.CrossRefGoogle Scholar
[6]Sims, B., ‘A support map characterization of the Opial conditions’, Proc. Centre Math. Anal. Austral. Nat. Univ. 9 (1985), 259–264.Google Scholar
[7]Sims, B., ‘A class of spaces with the weak normal structure’, Bull. Austral. Math. Soc. 49 (1994), 523–528.CrossRefGoogle Scholar