On a generalized geometric constant and sufficient conditions for normal structure in Banach spaces

Dinarvand, Mina

doi:10.1016/s0252-9602(17)30068-1

Cited by 7 publications

(2 citation statements)

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“…Since then, many mathematicians have established that, under various geometric properties of a Banach space often measured by different geometric constants, normal structure or uniform normal structure of the space is guaranteed. For more details in this direction, we refer the reader to [10,11,12,13,14,15,16,17,21,25,28,29,30,31,32,36] and the references mentioned therein.…”

Section: Introductionmentioning

confidence: 99%

On a General Class of Geometric Constants and Normal Structure in Banach Spaces

Dinarvand

2022

Preprint

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In this paper, we establish the lower bounds for the weakly convergent sequence coefficient WCS(X) of a Banach space X, in terms of the family of geometric constants Cλ,p(X), the coefficient of weak orthogonality µ(X) and the generalized García-Falset coefficient R(1, X). By mean of these bounds, we identify some geometrical properties implying normal structure. Moreover, some sufficient conditions which imply uniform normal structure are presented. Our results significantly generalize and improve many known results in the literature.Mathematics Subject Classification (2020): Primary 46B20; Secondary 47H09.

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Section: Introductionmentioning

confidence: 99%

On a General Class of Geometric Constants and Normal Structure in Banach Spaces

Dinarvand

2022

Preprint

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“…For a Banach space X, several studies on the James constant J(X) and also on the von Neumann-Jordan constant C NJ (X) have been conducted by Gao [1,2], Yang and Wang [3], and Kato, Maligranda and Takahashi [4,5]. Interested readers in this field are advised to see the work presented in [6][7][8][9][10][11] and the references mentioned therein.…”

Section: Introductionmentioning

confidence: 99%

On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Liu¹,

Li²

2021

Mathematics

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In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

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