Contractive Fixed Points in a Rectangular Metric Space and Applications
Branciari (2000) introduced the notion of a rectangular metric space ({\it rms}) as a generalization of a metric space and proved the well-known Banach's contraction mapping theorem in an {\it rms}, which was further generalized by Sarma et al. (2009) through a Ciric contraction. A fixed point...
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University of Maragheh
2025-04-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_719499_c9bf25a61d64bcb4983735d38e1ceef8.pdf |
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| author | G Shanmuga Sundari T Phaneendra |
| author_facet | G Shanmuga Sundari T Phaneendra |
| author_sort | G Shanmuga Sundari |
| collection | DOAJ |
| description | Branciari (2000) introduced the notion of a rectangular metric space ({\it rms}) as a generalization of a metric space and proved the well-known Banach's contraction mapping theorem in an {\it rms}, which was further generalized by Sarma et al. (2009) through a Ciric contraction. A fixed point $p$ of a self-map $f$ is a contractive fixed point (Edelstein, 1962), provided all the Picard's iterates $x,fx,f^2x, \ldots $ converge to $p$. In the first part of the paper, contractive fixed points of Banach and Ciric contractions are established in a rectangular metric space. Usually, it is shown that an appropriate Picard's iterative sequence with an arbitrary seed converges to a point, which is a unique fixed point. Rather than relying on the standard iterative procedure, in the next part of the paper, unique fixed points are obtained for Banach, Hardy-Roger and Ciric's contractions in a rectangular metric space through the rectangle inequality and the greatest lower bound property of real numbers. In the last part of the paper, two elegant problems of Volterra integral equations are presented with the necessary MATLAB interpretation. |
| format | Article |
| id | doaj-art-8a1a8f439b654314b0ffc5dbd9760019 |
| institution | OA Journals |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of Maragheh |
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| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-8a1a8f439b654314b0ffc5dbd97600192025-08-20T02:12:33ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002025-04-01222477210.22130/scma.2024.2031468.1757719499Contractive Fixed Points in a Rectangular Metric Space and ApplicationsG Shanmuga Sundari0T Phaneendra1Department of Mathematics, Vellore Institute of Technology, Vellore-632 014, Tamil Nadu, India.Department of Mathematics, Vellore Institute of Technology, Vellore-632 014, Tamil Nadu, India.Branciari (2000) introduced the notion of a rectangular metric space ({\it rms}) as a generalization of a metric space and proved the well-known Banach's contraction mapping theorem in an {\it rms}, which was further generalized by Sarma et al. (2009) through a Ciric contraction. A fixed point $p$ of a self-map $f$ is a contractive fixed point (Edelstein, 1962), provided all the Picard's iterates $x,fx,f^2x, \ldots $ converge to $p$. In the first part of the paper, contractive fixed points of Banach and Ciric contractions are established in a rectangular metric space. Usually, it is shown that an appropriate Picard's iterative sequence with an arbitrary seed converges to a point, which is a unique fixed point. Rather than relying on the standard iterative procedure, in the next part of the paper, unique fixed points are obtained for Banach, Hardy-Roger and Ciric's contractions in a rectangular metric space through the rectangle inequality and the greatest lower bound property of real numbers. In the last part of the paper, two elegant problems of Volterra integral equations are presented with the necessary MATLAB interpretation.https://scma.maragheh.ac.ir/article_719499_c9bf25a61d64bcb4983735d38e1ceef8.pdfrectangular metric spacecontraction type mappingsinfimum propertyfixed pointcontractive fixed pointvolterra integral equation |
| spellingShingle | G Shanmuga Sundari T Phaneendra Contractive Fixed Points in a Rectangular Metric Space and Applications Sahand Communications in Mathematical Analysis rectangular metric space contraction type mappings infimum property fixed point contractive fixed point volterra integral equation |
| title | Contractive Fixed Points in a Rectangular Metric Space and Applications |
| title_full | Contractive Fixed Points in a Rectangular Metric Space and Applications |
| title_fullStr | Contractive Fixed Points in a Rectangular Metric Space and Applications |
| title_full_unstemmed | Contractive Fixed Points in a Rectangular Metric Space and Applications |
| title_short | Contractive Fixed Points in a Rectangular Metric Space and Applications |
| title_sort | contractive fixed points in a rectangular metric space and applications |
| topic | rectangular metric space contraction type mappings infimum property fixed point contractive fixed point volterra integral equation |
| url | https://scma.maragheh.ac.ir/article_719499_c9bf25a61d64bcb4983735d38e1ceef8.pdf |
| work_keys_str_mv | AT gshanmugasundari contractivefixedpointsinarectangularmetricspaceandapplications AT tphaneendra contractivefixedpointsinarectangularmetricspaceandapplications |