Volume 38, Issue 2
Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application

Anal. Theory Appl., 38 (2022), pp. 232-242.

Published online: 2022-07

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• Abstract

In this paper, we prove fixed point theorem for weakly contractive mappings using locally $T$-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our fixed point results under universal relation reduces to Harjani and Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.

• Keywords

$\mathcal{R}$-continuity, locally $T$-transitive binary relation, weakly contractive map.

47H10, 54H25

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• TXT
@Article{ATA-38-232, author = {Gopi and Prasad and and 24079 and and Gopi Prasad and Ramesh Chandra and Dimri and and 24080 and and Ramesh Chandra Dimri}, title = {Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application}, journal = {Analysis in Theory and Applications}, year = {2022}, volume = {38}, number = {2}, pages = {232--242}, abstract = {

In this paper, we prove fixed point theorem for weakly contractive mappings using locally $T$-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our fixed point results under universal relation reduces to Harjani and Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0044}, url = {http://global-sci.org/intro/article_detail/ata/20800.html} }
TY - JOUR T1 - Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application AU - Prasad , Gopi AU - Dimri , Ramesh Chandra JO - Analysis in Theory and Applications VL - 2 SP - 232 EP - 242 PY - 2022 DA - 2022/07 SN - 38 DO - http://doi.org/10.4208/ata.OA-2017-0044 UR - https://global-sci.org/intro/article_detail/ata/20800.html KW - $\mathcal{R}$-continuity, locally $T$-transitive binary relation, weakly contractive map. AB -

In this paper, we prove fixed point theorem for weakly contractive mappings using locally $T$-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our fixed point results under universal relation reduces to Harjani and Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.

Gopi Prasad & Ramesh Chandra Dimri. (2022). Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application. Analysis in Theory and Applications. 38 (2). 232-242. doi:10.4208/ata.OA-2017-0044
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