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Guide Iterative Methods for Fixed Point Problems in Hilbert Spaces

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Density matrix unitary transformation

Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems.

On this basis we discuss the conditions under which particular methods converge.

Some results on variational inequalities and generalized equilibrium problems with applications

A large part of the results presented in this monograph can be found in various forms in the literature although several results presented here are new. We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems. In summary, I highly recommend this book to anyone interested in projection methods, their generalizations and recent developments.

Fixed point iteration method - idea and example

Bauschke, Mathematical Reviews, July, JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Lecture Notes in Mathematics Free Preview.

We establish the strong convergence of the proposed method for approximating a common element of the above defined sets under some suitable conditions. The results presented in this paper extend and improve some well-known corresponding results in the earlier and recent literature.

Source J.

Open Mathematics

Husain, Shamshad; Singh, Nisha. Read more about accessing full-text Buy article. Abstract Article info and citation First page References Abstract In this paper, a hybrid iterative algorithm is proposed for finding a common element of the set of common fixed points of finite family of nonexpansive mappings and the set of common solutions of the variational inequality for an inverse strongly monotone mapping on the real Hilbert space.

Article information Source J. Export citation. Export Cancel. References J.


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