<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergence in the same cases can be obtained on the basis of these lemmas.</p></abstract>

Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergence in the same cases can be obtained on the basis of these lemmas.

Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations...

Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations

Published Online: Dec 11, 2014

Page range: 3 - 16

Received: Jun 16, 2014

Accepted: Jul 30, 2014

DOI: https://doi.org/10.2478/awutm-2014-0001

Keywords
Recurrent inequalities, Fixed points, Iterative procedures

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations

Published Online: Dec 11, 2014

Page range: 3 - 16

Received: Jun 16, 2014

Accepted: Jul 30, 2014

DOI: https://doi.org/10.2478/awutm-2014-0001

KeywordsRecurrent inequalities, Fixed points, Iterative procedures

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Recurrent inequalities, Fixed points, Iterative procedures