<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Using the technique of enriching contractive type mappings, we introduce a more general concept of enriched Ćirić-Reich-Rus contraction than the one studied in [Berinde, V.; Păcurar, M. Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces. <italic>Carpathian J. Math.</italic> <bold>37</bold> (2021), no. 2, 173–184.] and provide convergence results for the Krasnoselskij iterative algorithm used to approximate their fixed points. Examples to illustrate the effectiveness of the new results as well as comparison to other classes of contractive type mappings existing in literature are also presented. In this context, we also conclude that Ćirić-Reich-Rus contractions form a class of unsaturated mappings.</p>
</abstract>

Using the technique of enriching contractive type mappings, we introduce a more general concept of enriched Ćirić-Reich-Rus contraction than the one studied in [Berinde, V.; Păcurar, M. Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces. Carpathian J. Math. 37 (2021), no. 2, 173–184.] and provide convergence results for the Krasnoselskij iterative algorithm used to approximate their fixed points. Examples to illustrate the effectiveness of the new results as well as comparison to other classes of contractive type mappings existing in literature are also presented. In this context, we also conclude that Ćirić-Reich-Rus contractions form a class of unsaturated mappings.

A new class of unsaturated mappings: Ćirić-Reich-Rus contractions

Academy of Romanian Scientists and Department of Mathematics and Computer Science

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

Department of Economics and Business Administration in German Language, Faculty of Economics and Business Administration

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"A new class of unsaturated mappings: Ćirić-Reich-Rus contractions"}

Using the technique of enriching contractive type mappings, we introduce a more general concept of enriched Ćirić-Reich-Rus contraction than the one studied in...

A new class of unsaturated mappings: Ćirić-Reich-Rus contractions

Published Online: Oct 08, 2022

Page range: 37 - 50

Received: Nov 30, 2021

Accepted: Jan 31, 2022

DOI: https://doi.org/10.2478/auom-2022-0033

Keywords
metric space, Banach contraction, Ćirić-Reich-Rus contraction, enriched Ćirić-Reich-Rus contraction, fixed point, Krasnoselskij iteration

© 2022 Vasile Berinde et al., published by Sciendo

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

A new class of unsaturated mappings: Ćirić-Reich-Rus contractions

Published Online: Oct 08, 2022

Page range: 37 - 50

Received: Nov 30, 2021

Accepted: Jan 31, 2022

DOI: https://doi.org/10.2478/auom-2022-0033

Keywordsmetric space, Banach contraction, Ćirić-Reich-Rus contraction, enriched Ćirić-Reich-Rus contraction, fixed point, Krasnoselskij iteration

© 2022 Vasile Berinde et al., published by Sciendo

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

Keywords
metric space, Banach contraction, Ćirić-Reich-Rus contraction, enriched Ćirić-Reich-Rus contraction, fixed point, Krasnoselskij iteration