On Moduli of Expansion of the Duality Mapping of Smooth Banach Spaces

Volume 3, Issue 4, 2002

Article 55

ON MODULI OF EXPANSION OF THE DUALITY MAPPING OF SMOOTH BANACH SPACES

FACULTY OF MATHEMATICS
UNIVERSITY OF BELGRADE
YU-11000, YUGOSLAVIA.
E-Mail:

Received 5 April, 2002; Accepted 20 May, 2002.
Communicated by: S.S. Dragomir

ABSTRACT. Let X be a Banach space which is uniformly convex and uniformly smooth. We introduce the lower and upper moduli of expansion of the dual mapping J of the space X. Some estimation of certain well-known moduli (convexity, smoothness and flatness) and two new moduli introduced in [5] are described with this new moduli of expansion.

[5] P.M. MILICIC, The angle modulus of the deformation of a normed space, Riv. Mat. Univ. Parma, (6) 3(2002), 101-111.

Key words:
Uniformly convex (smooth) Banach space, Angle of modulus convexity (smoothness), Lower (upper) modulus of expansion.

2000 Mathematics Subject Classification:
46B20, 46C15, 51K05.

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