Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 2, pp. 285-295 (2015)

Iterative algorithms for determining multiplicative inverses in Banach algebras

Chiapo R. Sam

University of Botswana

Abstract: By using Banach's fixed point theorem and properties of strong derivatives of nonlinear mappings, we prove some convergence theorems and error estimations of a family of iterative methods of arbitrary order for determining the inverse elements in a unital Bananch algebra.

Keywords: Banach algebra, fixed point theorem, iteration, multiplicative inverse.

Classification (MSC2000): 47A05; 47H10, 65J10, 65J15, 65J22

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