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71.
Let A2(X) be the constant introduced by Baronti, Casini and Papini. This paper discusses the constant A2(X) and states an estimate in terms of the James constant. The estimate enables us to improve an inequality between the James and von Neumann-Jordan constants. 相似文献
72.
Ken-Ichi Mitani Kichi-Suke Saito 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):310-5247
In [M. Kato and L. Maligranda, On James and Jordan–von Neumann constants of Lorentz sequence spaces, J. Math. Anal. Appl. 258 (2001) 457–465], it is an open problem to compute the James constant of the dual space of two dimensional Lorentz sequence space d(2)(w,q). In this paper, we shall determine the dual norm of d(2)(w,q) and completely compute the James constant of d(2)(w,q). 相似文献
73.
A new condition for mappings, called condition (C), which is more general than nonexpansiveness, was recently introduced by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. Following the idea of Kirk and Massa Theorem in [W.A. Kirk, S. Massa, Remarks on asymptotic and Chebyshev centers, Houston J. Math. 16 (1990) 364-375], we prove a fixed point theorem for mappings with condition (C) on a Banach space such that its asymptotic center in a bounded closed and convex subset of each bounded sequence is nonempty and compact. This covers a result obtained by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. We also present fixed point theorems for this class of mappings defined on weakly compact convex subsets of Banach spaces satisfying property (D). Consequently, we extend the results in [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] to many other Banach spaces. 相似文献
74.
Let CNJ(X) and J(X) be the von Neumann-Jordan and James constants of a Banach space X, respectively. We shall show that CNJ(X)?J(X), where equality holds if and only if X is not uniformly non-square. This answers affirmatively to the question in a recent paper by Alonso et al. [J. Alonso, P. Martín, P.L. Papini, Wheeling around von Neumann-Jordan constant in Banach spaces, Studia Math. 188 (2008) 135-150]. This inequality looks quite simple and covers all the preceding results. In particular this is much stronger than Maligranda's conjecture: . 相似文献