Displaying similar documents to “Iterations converging to distinct solutions of some nonlinear operator equations in Banach space.”

On the Halley method in Banach spaces

Ioannis K. Argyros, Hongmin Ren (2012)

Applicationes Mathematicae

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We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.

A result on segmenting Jungck–Mann iterates

Memudu Olaposi Olatinwo (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement...