多项式型非自治迭代方程的凹凸解

Convex solutions of polynomial-like nonautonomous iterative equations

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.