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Successive approximations

  • M. A. Krasnosel’skii
  • G. M. Vainikko
  • P. P. Zabreiko
  • Ya. B. Rutitskii
  • V. Ya. Stetsenko

Abstract

1.1. Contraction operators. Let A be an operator defined on a set A in a Banach space E, satisfying a Lipschitz condition
$$\left\| {Ax - Ay} \right\| \le q\left\| {x - y} \right\|\left( {x,y \in \Re } \right).$$
(1.1)
If q < 1, A is called a contraction operator (or contracting operator).

Keywords

Banach Space Spectral Radius Monotone Operator Successive Approximation Lipschitz Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Wolters-Noordhoff Publishing, Groningen 1972

Authors and Affiliations

  • M. A. Krasnosel’skii
  • G. M. Vainikko
  • P. P. Zabreiko
  • Ya. B. Rutitskii
  • V. Ya. Stetsenko

There are no affiliations available

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