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The computation of iteration is difficult for general functions (even for some simple functions such as linear fractional functions). In this paper, we discuss fractional polynomial function and use the method of conjugate similitude to obtain its expression of general iterate of order<jats:italic>n<\/jats:italic>under two different conditions. Furthermore, we also give iterative roots of order<jats:italic>n<\/jats:italic>for the function under two different conditions.<\/jats:p>","DOI":"10.1155\/2012\/365956","type":"journal-article","created":{"date-parts":[[2012,6,13]],"date-time":"2012-06-13T04:06:00Z","timestamp":1339560360000},"page":"1-10","source":"Crossref","is-referenced-by-count":2,"title":["Iteration and Iterative Roots of Fractional Polynomial Function"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xiao-hua","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Leshan Normal University, Leshan, Sichuan 614004, China"}]}],"member":"98","reference":[{"issue":"4","key":"1","first-page":"483","volume":"30","year":"1980-1981","journal-title":"Australian Mathematical Society Journal Series A"},{"issue":"2","key":"2","first-page":"197","volume":"6","year":"1981-1982","journal-title":"Annales Academiae Scientiarum Fennicae. Series A I. 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