01115nas a2200205   4500000000100000000000100001008004100002260001200043653002200055653002200077653002700099100002000126700002000146245006200166856009800228300001000326490000600336520055300342022001400895       2015                            d  c09/201510aNewton’s Method10aLocal Convergence10aSteffensen-type Method1 aIoannis Argyros1 aSanthosh George00aBall Convergence for Steffensen-type Fourth-order Methods  uhttp://www.ijimai.org/JOURNAL/sites/default/files/files/2015/08/ijimai20153_4_7_pdf_73265.pdf  a37-420 v33 aWe present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.  a1989-1660