Volume 3,  Issue 4, 2002

Article 55

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

PAVLE M. MILICIC

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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