01129nas a2200217   4500000000100000000000100001008004100002260001200043653002500055653002200080653001700102653002200119100002000141700002200161245007400183856009800257300001000355490000600365520052600371022001400897       2015                            d  c09/201510aJarratt-type Methods10aNewton’s Method10aBanach Space10aLocal Convergence1 aIoannis Argyros1 aDaniel González00aLocal Convergence for an Improved Jarratt-type Method in Banach Space  uhttp://www.ijimai.org/JOURNAL/sites/default/files/files/2015/08/ijimai20153_4_4_pdf_25787.pdf  a20-250 v33 aWe present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.  a1989-1660