Existence,construction and extension of continuous solutions of an iterative equation with multiplication  

作　　者：Chaitanya Gopalakrishna Murugan Veerapazham Suyun Wang Weinian Zhang 

机构地区：[1]Statistics and Mathematics Unit,Indian Statistical Institute,R.V.College Post,Bengaluru 560059,India [2]Department of Mathematical and Computational Sciences,National Institute of Technology Karnataka,Surathkal,Mangalore 575025,India [3]School of Mathematics,Lanzhou City University,Lanzhou 730070,China [4]School of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Science China Mathematics》2023年第10期2261-2276,共16页中国科学：数学（英文版）

基　　金：supported by National Institute of Technology Karnataka Surathkal through Senior Research Fellowship and Indian Statistical Institute Bangalore in the form of a Visiting Scientist position through the Jagadish Chandra Bose Fellowship of Professor Badekkila Venkataramana Rajarama Bhat;supported by Science and Engineering Research Board,Department of Science and Technology,Government of India(Grant No.ECR/2017/000765);supported by National Natural Science Foundation of China(Grant Nos.11831012,12171336 and 11821001).

摘　　要：The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multiplication of iterates of the unknown function.First,we use an exponential conjugation to reduce the equation on R+to the form of the linear combination on R,but those known results on the linear combination were obtained on a compact interval or a neighborhood near a fixed point.We use the Banach contraction principle to give the existence,uniqueness and continuous dependence of continuous solutions on R+that are Lipschitzian on their ranges,and construct its continuous solutions on R_(+)sewing piece by piece.We technically extend our results on R_(+)to R_(-)and show that none of the pairs of solutions obtained on R+and R_(-)can be combined at the origin to get a continuous solution of the equation on the whole R,but can extend those given on R+to obtain continuous solutions on the whole R.

关 键 词：functional equation ITERATION nonlinear combination contraction principle 

分 类 号：O241.6[理学—计算数学]