We replace Chebyshev's method for solving equations requiring the second derivative by a Chebyshevtype second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast to the Chebyshev method using hypotheses on the second derivative. This way we extend the applicability of the method. Numerical examples are also used to test the convergence criteria and to obtain error bounds and also the radius of convergence.
Chebyshev method, Newton method, Fr\'echet derivative, Local convergence, Divided differences
Primary Language  English 

Subjects  Mathematical Sciences 
Journal Section  Articles 
Authors 

Publication Date  September 30, 2018 
Submission Date  July 6, 2018 
Acceptance Date  August 17, 2018 
Published in Issue  Year 2018 Volume: 1 Issue: 1 
Bibtex  @research article { cams441220, journal = {Communications in Advanced Mathematical Sciences}, issn = {26514001}, address = {}, publisher = {Emrah Evren KARA}, year = {2018}, volume = {1}, number = {1}, pages = {84  90}, doi = {10.33434/cams.441220}, title = {Local convergence for composite Chebyshevtype methods}, key = {cite}, author = {Argyros, İoannis K and George, Santhosh} } 
APA  Argyros, İ. K. & George, S. (2018). Local convergence for composite Chebyshevtype methods . Communications in Advanced Mathematical Sciences , 1 (1) , 8490 . DOI: 10.33434/cams.441220 
MLA  Argyros, İ. K. , George, S. "Local convergence for composite Chebyshevtype methods" . Communications in Advanced Mathematical Sciences 1 (2018 ): 8490 <https://dergipark.org.tr/en/pub/cams/issue/39351/441220> 
Chicago  Argyros, İ. K. , George, S. "Local convergence for composite Chebyshevtype methods". Communications in Advanced Mathematical Sciences 1 (2018 ): 8490 
RIS  TY  JOUR T1  Local convergence for composite Chebyshevtype methods AU  İoannis KArgyros, SanthoshGeorge Y1  2018 PY  2018 N1  doi: 10.33434/cams.441220 DO  10.33434/cams.441220 T2  Communications in Advanced Mathematical Sciences JF  Journal JO  JOR SP  84 EP  90 VL  1 IS  1 SN  26514001 M3  doi: 10.33434/cams.441220 UR  https://doi.org/10.33434/cams.441220 Y2  2018 ER  
EndNote  %0 Communications in Advanced Mathematical Sciences Local convergence for composite Chebyshevtype methods %A İoannis K Argyros , Santhosh George %T Local convergence for composite Chebyshevtype methods %D 2018 %J Communications in Advanced Mathematical Sciences %P 26514001 %V 1 %N 1 %R doi: 10.33434/cams.441220 %U 10.33434/cams.441220 
ISNAD  Argyros, İoannis K , George, Santhosh . "Local convergence for composite Chebyshevtype methods". Communications in Advanced Mathematical Sciences 1 / 1 (September 2018): 8490 . https://doi.org/10.33434/cams.441220 
AMA  Argyros İ. K. , George S. Local convergence for composite Chebyshevtype methods. Communications in Advanced Mathematical Sciences. 2018; 1(1): 8490. 
Vancouver  Argyros İ. K. , George S. Local convergence for composite Chebyshevtype methods. Communications in Advanced Mathematical Sciences. 2018; 1(1): 8490. 
IEEE  İ. K. Argyros and S. George , "Local convergence for composite Chebyshevtype methods", Communications in Advanced Mathematical Sciences, vol. 1, no. 1, pp. 8490, Sep. 2018, doi:10.33434/cams.441220 