AI 中文总结
该研究统一多项式压缩映射与Z压缩映射思想，引入多项式Z压缩映射，利用仿真函数证明其两个不动点结果，还将其应用于L^p(0,π)中边值问题解的存在性与唯一性讨论。
AI 中文摘要
本文通过统一多项式压缩映射与$\boldsymbol{\textit{Z}}$压缩映射的思想，引入了多项式$\boldsymbol{\textit{Z}}$压缩映射，并给出示例以证明其有效性与新颖性。主要地，我们利用仿真函数证明了多项式$\boldsymbol{\textit{Z}}$压缩映射的两个不动点结果。最后，在适当假设下，我们运用主要结果讨论了$L^p(0,\boldsymbol{\textit{π}})$中边值问题解的存在性与唯一性，并给出具体实例。
英文摘要
In this paper, we introduce polynomial $\mathcal{Z}$-contraction by unifying the ideas of polynomial contraction and $\mathcal{Z}$-contraction and also provide demonstrative examples to show the effectiveness and novelty. Chiefly, we prove two fixed point results for polynomial $\mathcal{Z}$-contraction employing simulation functions. Lastly, we utilize our main result to discuss the existence and uniqueness of solution for boundary value problem with a concrete example in $L^p(0,π)$ under suitable assumptions.
Comments16 pages, 1 figure(two sub figures)
