<p>In this paper, for any <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1277_Article_IEq4.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="77" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda \ge 1,~R_\lambda ^2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>≥</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt" /> <msubsup> <mi>R</mi> <mi>λ</mi> <mn>2</mn> </msubsup> </mrow> </math></EquationSource> </InlineEquation> is the Banaś-Frączek space. The exact value of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1277_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">$L_\textrm{YJ}(\xi ,\eta ,X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mtext>YJ</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi>ξ</mi> <mo>,</mo> <mi>η</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for this space will be calculated. Specifically, <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1277_Article_IEq6.gif" Format="GIF" Height="27" Rendition="HTML" Resolution="72" Type="Linedraw" Width="233" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{\textrm{YJ}}( \xi , \eta , R_{\lambda }^{2}) = 1+ \frac{2\xi \eta }{\xi ^{2}+ \eta ^{2}}( 1- \frac{1}{\lambda ^{2}})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mtext>YJ</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi>ξ</mi> <mo>,</mo> <mi>η</mi> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mi>λ</mi> </mrow> <mn>2</mn> </msubsup> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>ξ</mi> <mi>η</mi> </mrow> <mrow> <msup> <mi>ξ</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>η</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mn>1</mn> <msup> <mi>λ</mi> <mn>2</mn> </msup> </mfrac> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is the result thereafter through meticulous computation.</p>

On the $L_\textrm{Y J}(\xi ,\eta ,X)$ constant for the Banaś-Frączek space

期刊论文
发表日期：

2025年7月15日

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Yuxin Wang,
Qi Liu,
Linhui Chen,
Xiewei Tan,
Muhammad Sarfraz

摘要

In this paper, for any $\lambda \ge 1,~R_\lambda ^2$ $λ \geq 1, R_{λ}^{2}$ is the Banaś-Frączek space. The exact value of $L_\textrm{YJ}(\xi ,\eta ,X)$ $L_{YJ} (ξ, η, X)$ for this space will be calculated. Specifically, $L_{\textrm{YJ}}( \xi , \eta , R_{\lambda }^{2}) = 1+ \frac{2\xi \eta }{\xi ^{2}+ \eta ^{2}}( 1- \frac{1}{\lambda ^{2}})$ $L_{YJ} (ξ, η, R_{λ}^{2}) = 1 + \frac{2 ξ η}{ξ^{2} + η^{2}} (1 - \frac{1}{λ^{2}})$ is the result thereafter through meticulous computation.

On the \(L_\textrm{Y J}(\xi ,\eta ,X)\) constant for the Banaś-Frączek space

摘要