# Steffensen Methods for Solving Generalized Equations

Argyros, Ioannis K.; Hilout, Saïd

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 2, page 455-466
- ISSN: 1310-6600

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topArgyros, Ioannis K., and Hilout, Saïd. "Steffensen Methods for Solving Generalized Equations." Serdica Mathematical Journal 34.2 (2008): 455-466. <http://eudml.org/doc/281512>.

@article{Argyros2008,

abstract = {2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].},

author = {Argyros, Ioannis K., Hilout, Saïd},

journal = {Serdica Mathematical Journal},

keywords = {Steffensen's Method; Banach Space; Set-Valued Mapping; Generalized Equations; Aubin Continuity; Divided Difference; Newton's Method; Steffensen's method; Banach space; set-valued mapping; generalized equations; Aubin continuity; divided difference; Newton's method; power series; overconvergence; distribution of the zeroes},

language = {eng},

number = {2},

pages = {455-466},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Steffensen Methods for Solving Generalized Equations},

url = {http://eudml.org/doc/281512},

volume = {34},

year = {2008},

}

TY - JOUR

AU - Argyros, Ioannis K.

AU - Hilout, Saïd

TI - Steffensen Methods for Solving Generalized Equations

JO - Serdica Mathematical Journal

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 34

IS - 2

SP - 455

EP - 466

AB - 2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].

LA - eng

KW - Steffensen's Method; Banach Space; Set-Valued Mapping; Generalized Equations; Aubin Continuity; Divided Difference; Newton's Method; Steffensen's method; Banach space; set-valued mapping; generalized equations; Aubin continuity; divided difference; Newton's method; power series; overconvergence; distribution of the zeroes

UR - http://eudml.org/doc/281512

ER -

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