TY - JOUR
T1 - Local convergence of a novel eighth order method under hypotheses only on the first derivative
AU - Argyros, Ioannis K.
AU - George, Santhosh
AU - Erappa, Shobha M.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We expand the applicability of eighth order-iterative method stud- ied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
AB - We expand the applicability of eighth order-iterative method stud- ied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
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U2 - 10.22034/kjm.2019.88082
DO - 10.22034/kjm.2019.88082
M3 - Article
AN - SCOPUS:85073193150
SN - 2423-4788
VL - 5
SP - 96
EP - 107
JO - Khayyam Journal of Mathematics
JF - Khayyam Journal of Mathematics
IS - 2
ER -