Existence of continuous solutions and stability for a general iterative functional equation

作者：

Highlights：

• We investigate the existence of solutions for a general form iterative equation.

• The stability of those solutions is also discussed.

• We generalize the work from a linear combination of iterates to nonlinear.

• An algorithm is presented to compute the piecewise linear solutions.

摘要

•We investigate the existence of solutions for a general form iterative equation.•The stability of those solutions is also discussed.•We generalize the work from a linear combination of iterates to nonlinear.•An algorithm is presented to compute the piecewise linear solutions.

论文关键词：37E05,39B12,26A18,Iterative equation,Leading coefficient problem,Hyers–Ulam stability,Polygonal function

论文评审过程：Received 7 February 2013, Revised 12 October 2013, Available online 23 October 2013.

论文官网地址：https://doi.org/10.1016/j.cam.2013.10.029