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An extension of a simply inequality between von Neumann–Jordan and James constants in Banach spaces

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Abstract

For a non-trivial Banach space X, let J(X), C NJ(X), C (p)NJ (X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C (p)NJ (X) ≤ J(X) with p ≥ 2, which covers the well-known inequality C NJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.

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Authors and Affiliations

  1. College of Mathematics and Information Science, He’nan Normal University, Xinxiang, 453007, P. R. China

    Chang Sen Yang

  2. Department of Mathematics, Luoyang Normal University, Luoyang, 471022, P. R. China

    Feng Hui Wang

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  1. Chang Sen Yang
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  2. Feng Hui Wang
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Correspondence to Chang Sen Yang.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11271112 and 11201127) Innovation Scientists and Technicians Troop Construction Projects of He’nan Province (Grant No. 114200510011, C20150027)

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Yang, C.S., Wang, F.H. An extension of a simply inequality between von Neumann–Jordan and James constants in Banach spaces. Acta. Math. Sin.-English Ser. 33, 1287–1296 (2017). https://doi.org/10.1007/s10114-017-6211-6

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  • DOI: https://doi.org/10.1007/s10114-017-6211-6

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