Some aspects of generalized von Neumann-Jordan type constant

• Published in: AIMS mathematics Vol. 6; no. 6; pp. 6309 - 6321
• Main Authors: Liu, Qi, Din, Anwarud, Li, Yongjin
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: banach spaces; geometric constants; normal structure
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021370

In recent times, Takahashi has introduced von Neumann-Jordan type constants $ C_{-\infty}(X) $. In the present manuscript, we establish a novel geometric constant $ C_{-\infty}(a, X) $ in a Banach space $ X $. Next, it is shown that $ \frac{1}{2}+\frac{2a}{4+a^2}\leqslant C_{-\infty}(a, X)\leqslant 1 $ for all $ a\geqslant0 $. Further, between the generalized James constant $ J(a, X) $ and $ C_{-\infty}(a, X) $, a relationship is investigated. For uniform normal structure, a few sufficient conditions were established. Finally, we investigate some relations between the two constants $ N(X) $ and $ C_{-\infty}(a, X) $.