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Volume 39, Issue 2
Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space

Shaoyuan Xu, Suyu Cheng & Yan Han

DOI: 10.4208/ata.OA-2018-0022

Anal. Theory Appl., 39 (2023), pp. 191-200.

Published online: 2023-06

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  • Abstract

Let $(X, d)$ be a cone metric space and $T : X → X$ be a mapping. In this paper, we shall introduce the concept of strong $T$-stability of fixed point iteration procedures with respect to $T$ in cone metric spaces. Also, we will investigate some meaningful results on strong $T$-stability of Picard iterations in cone metric spaces without the assumption of normality. Our main results improve and generalize some related results in the literature.

  • Keywords

Strong $T$-stability, Picard iteration, non-normal cone, cone metric space.

  • AMS Subject Headings

54H25, 47H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-39-191, author = {Xu , ShaoyuanCheng , Suyu and Han , Yan}, title = {Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {2}, pages = {191--200}, abstract = {

Let $(X, d)$ be a cone metric space and $T : X → X$ be a mapping. In this paper, we shall introduce the concept of strong $T$-stability of fixed point iteration procedures with respect to $T$ in cone metric spaces. Also, we will investigate some meaningful results on strong $T$-stability of Picard iterations in cone metric spaces without the assumption of normality. Our main results improve and generalize some related results in the literature.

}, issn = {1573-8175}, doi = {https://doi.org/ 10.4208/ata.OA-2018-0022}, url = {http://global-sci.org/intro/article_detail/ata/21823.html} }
TY - JOUR T1 - Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space AU - Xu , Shaoyuan AU - Cheng , Suyu AU - Han , Yan JO - Analysis in Theory and Applications VL - 2 SP - 191 EP - 200 PY - 2023 DA - 2023/06 SN - 39 DO - http://doi.org/ 10.4208/ata.OA-2018-0022 UR - https://global-sci.org/intro/article_detail/ata/21823.html KW - Strong $T$-stability, Picard iteration, non-normal cone, cone metric space. AB -

Let $(X, d)$ be a cone metric space and $T : X → X$ be a mapping. In this paper, we shall introduce the concept of strong $T$-stability of fixed point iteration procedures with respect to $T$ in cone metric spaces. Also, we will investigate some meaningful results on strong $T$-stability of Picard iterations in cone metric spaces without the assumption of normality. Our main results improve and generalize some related results in the literature.

Shaoyuan Xu, Suyu Cheng & Yan Han. (2023). Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space. Analysis in Theory and Applications. 39 (2). 191-200. doi: 10.4208/ata.OA-2018-0022
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