Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 20
• Main Authors: Sahu, DR, Singh, Krishna Kumar, Singh, Vipin Kumar
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 09.05.2012; Springer Nature B.V
• Subjects: Algorithms; Analysis; Applications of Mathematics; Banach space; Classification; Convergence; Differential Geometry; Estimates; Mathematical analysis; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Newton methods; Operators; Research Article; Topology; fixed point; Fréchet derivative; Newton's method; nonlinear operator equations; Banach contraction theorem; quasi-contraction; operator
• ISSN: 1687-1812; 1687-1820; 1687-1812; 2730-5422
• DOI: 10.1186/1687-1812-2012-78

It is well known that the rate of convergence of S -iteration process introduced by Agarwal et al. (pp. 61-79) is faster than Picard iteration process for contraction operators. Following the ideas of S -iteration process, we introduce some Newton-like algorithms to solve the non-linear operator equation in Banach space setting. We study the semi-local as well as local convergence analysis of our algorithms. The rate of convergence of our algorithms are faster than the modified Newton method. Mathematics Subject Classification 2010: 49M15; 65K10; 47H10.