| 多项式型非自治迭代方程的凹凸解 |
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| 引用本文： | 陈烨明,曾莹莹.多项式型非自治迭代方程的凹凸解[J].四川大学学报(自然科学版),2023,60(4):041005. |
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| 作者姓名： | 陈烨明 曾莹莹 |
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| 作者单位： | 四川大学数学学院,四川师范大学数学科学学院/可视化计算与虚拟现实四川省重点实验室 |
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| 基金项目： | 四川省科技计划资助项目(2022JDTD0019) |
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| 摘 要： | 迭代是同一函数的重复运算. 比通常的迭代更复杂的是有不同函数参与的非自治迭代. 本文讨论了一类包含非自治迭代的线性组合的函数方程, 即多项式型非自治迭代方程. 在前人给出的连续递增解基础上，本文进一步研究解的凹凸性, 给出了凹凸解的存在性、唯一性及连续依赖性.
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| 关 键 词： | 非自治迭代 凸性 差商 |
| 收稿时间： | 2022/7/11 0:00:00 |
| 修稿时间： | 2022/9/19 0:00:00 |
Convex solutions of polynomial-like nonautonomous iterative equations |
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| CHEN Ye-Ming and ZENG Ying-Ying.Convex solutions of polynomial-like nonautonomous iterative equations[J].Journal of Sichuan University (Natural Science Edition),2023,60(4):041005. |
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| Authors: | CHEN Ye-Ming and ZENG Ying-Ying |
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| Institution: | School of Mathematics, Sichuan University,School of Mathematical Science/VC & VR Key Lab of Sichuan Province, Sichuan Normal University |
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| Abstract: | Iteration is repetition of same function. Iteration with different functions, called nonautonomous iteration, is a more complex one. In this paper, we consider a class of functional equations with linear combination of nonautonomous iterations, namely the polynomial-like nonautonomous iterative equations. Based on some known results, the existence, uniqueness and continuous dependence on the functions and coefficients are studied. |
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| Keywords: | Nonautonomous iteration Concavity Divided difference |
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