<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we introduce and study the class of <italic>enriched strictly pseudocontractive mappings</italic> in Hilbert spaces and extend some convergence theorems, i.e., Theorem 12 in [Brow-der, F. E., Petryshyn, W. V., <italic>Construction of fixed points of nonlinear mappings in Hilbert space</italic>, J. Math. Anal. Appl. <bold>20</bold> (1967), 197–228] and Theorem 3.1 in [Marino, G., Xu, H.-K., <italic>Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces</italic>, J. Math. Anal. Appl. <bold>329</bold> (2007), no. 1, 336–346], from the class of strictly pseudocontractive mappings to that of enriched strictly pseudocontractive mappings and thus include many other important related results from literature as particular cases.</p></abstract>

In this paper, we introduce and study the class of enriched strictly pseudocontractive mappings in Hilbert spaces and extend some convergence theorems, i.e., Theorem 12 in [Brow-der, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 3.1 in [Marino, G., Xu, H.-K., Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), no. 1, 336–346], from the class of strictly pseudocontractive mappings to that of enriched strictly pseudocontractive mappings and thus include many other important related results from literature as particular cases.

Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators

Department of Mathematics and Computer Science

Technical University of Cluj-Napoca, North University Center at Baia Mare

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, we introduce and study the class of enriched strictly pseudocontractive mappings in Hilbert spaces and extend some convergence theorems, i.e.,...

Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators

Published Online: Apr 30, 2020

Page range: 13 - 27

DOI: https://doi.org/10.2478/awutm-2018-0013

Keywords
Hilbert space, strictly pseudocontractive mapping, enriched strictly pseudocontractive mapping, fixed point, Krasnoselskij iterative algorithm, weak convergence, strong convergence

© 2018 Vasile Berinde, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators

Published Online: Apr 30, 2020

Page range: 13 - 27

DOI: https://doi.org/10.2478/awutm-2018-0013

KeywordsHilbert space, strictly pseudocontractive mapping, enriched strictly pseudocontractive mapping, fixed point, Krasnoselskij iterative algorithm, weak convergence, strong convergence

© 2018 Vasile Berinde, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hilbert space, strictly pseudocontractive mapping, enriched strictly pseudocontractive mapping, fixed point, Krasnoselskij iterative algorithm, weak convergence, strong convergence