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Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces

AbstractLet "Equation missing" be an arbitrary real Banach space and "Equation missing" a nonempty, closed, convex (not necessarily bounded) subset of "Equation missing". If "Equation missing" is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant "Equation missing", then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of "Equation missing".

Springer Science and Business Media LLC

GVR Babu KNVV Vara Prasad

Fixed Point Theory and Applications

2007

Title: Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces

Description:

AbstractLet "Equation missing" be an arbitrary real Banach space and "Equation missing" a nonempty, closed, convex (not necessarily bounded) subset of "Equation missing".

If "Equation missing" is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant "Equation missing", then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration.

It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of "Equation missing".

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Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces

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