Korean J. Math.  Vol 27, No 4 (2019)  pp.1005-1025
DOI: https://doi.org/10.11568/kjm.2019.27.4.1005

Convergence of a continuation method under majorant conditions}

Shwet Nisha, P. K. Parida, Chandni Kumari


The paper is devoted to study local convergence of a continuation method under the assumption of majorant conditions. The method is used to approximate a zero of an operator in Banach space and is of third order. It is seen that the famous Kantorovich-type and Smale-type conditions are special cases of our majorant conditions. This infers that our result is a generalized one in comparison to results based on Kantorovich-type and Smale-type conditions. Finally a number of numerical examples have been computed to show applicability of the convergence analysis.


Continuation method; Majorant conditions; Kantorovich-type convergence criterion; Smale-type convergence criterion

Subject classification

65D10;65G99; 65K10;47H17;49M15


This work was supported by Central University of Jharkhand.

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