多项式型非自治迭代方程的凹凸解  

Convex solutions of polynomial-like nonautonomous iterative equations

作　　者：陈烨明 曾莹莹 CHEN Ye-Ming;ZENG Ying-Ying(School of Mathematics,Sichuan University,Chengdu 610064,China;School of Mathematical Sciences/V.C.&V.R.Key Lab of Sichuan Province,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川大学数学学院,成都610064 [2]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,成都610068

出　　处：《四川大学学报（自然科学版）》2023年第4期33-38,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技计划资助项目(2022JDTD0019)。

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运算的非自治迭代.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的基础上,本文进一步研究了解的凹凸性,给出了凹凸解的存在性、唯一性及连续依赖性.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 polynomial-like nonautonomous iterative equations.Based on some known results,the existence,uniqueness and continuous dependence of the convex solutions on the iterations and coefficients are studied.

关 键 词：非自治迭代 凸性 差商 

分 类 号：O178[理学—数学]