<p>Takahashi introduced the James type constant <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal{J}_{\mathcal{X}, t}(\tau)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">J</mi> <mrow> <mi mathvariant="script">X</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Motivated by this, we define a skew James type constant <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal{J}_{ t}[\tau,\mathcal{X}]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">J</mi> <mi>t</mi> </msub> <mrow> <mo stretchy="false">[</mo> <mi>τ</mi> <mo>,</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> as a natural generalization of the classical constant. We establish its equivalent representations and fundamental properties in Banach spaces. Furthermore, we examine the relationship between the constant <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal{J}_{ t}[\tau,\mathcal{X}]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">J</mi> <mi>t</mi> </msub> <mrow> <mo stretchy="false">[</mo> <mi>τ</mi> <mo>,</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and the modulus of convexity. Finally, we introduce a new geometric constant <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathcal{G}_t(\mathcal{X})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">G</mi> <mi>t</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and establish several of its properties.</p>

The skew James type constant in Banach spaces

期刊论文
发表日期：

2026年7月29日

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Z.-Y. Rao,
Q. Wu,
Q. Liu,
Q.-C. Ni,
Y.-X. Wang

摘要

Takahashi introduced the James type constant $\mathcal{J}_{\mathcal{X}, t}(\tau)$ $J_{X, t} (τ)$ . Motivated by this, we define a skew James type constant $\mathcal{J}_{ t}[\tau,\mathcal{X}]$ $J_{t} [τ, X]$ as a natural generalization of the classical constant. We establish its equivalent representations and fundamental properties in Banach spaces. Furthermore, we examine the relationship between the constant $\mathcal{J}_{ t}[\tau,\mathcal{X}]$ $J_{t} [τ, X]$ and the modulus of convexity. Finally, we introduce a new geometric constant $\mathcal{G}_t(\mathcal{X})$ $G_{t} (X)$ and establish several of its properties.