Fixed point theorems for weak, partial, Bianchini and Chatterjea-Bianchini contractions in semimetric spaces with triangle functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910769017257984 |
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| author | Bisht, Ravindra K. Petrov, Evgen O. |
| author_facet | Bisht, Ravindra K. Petrov, Evgen O. |
| contents | This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. Páles, building on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515-524 (2017)]. By applying this concept, the study revises several well-known fixed point theorems in metric spaces, extending their applicability to semimetric spaces with triangle functions. The paper focuses on general theorems involving weak, partial, Bianchini and Chatterjea-Bianchini contractions, deriving corollaries relevant to metric spaces, $b$-metric spaces, ultrametric spaces, and distance spaces with power triangle functions. Notably, several new and interesting findings emerge in the context of weak and partial contractions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fixed point theorems for weak, partial, Bianchini and Chatterjea-Bianchini contractions in semimetric spaces with triangle functions Bisht, Ravindra K. Petrov, Evgen O. General Topology Primary 47H10, Secondary 47H09 This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. Páles, building on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515-524 (2017)]. By applying this concept, the study revises several well-known fixed point theorems in metric spaces, extending their applicability to semimetric spaces with triangle functions. The paper focuses on general theorems involving weak, partial, Bianchini and Chatterjea-Bianchini contractions, deriving corollaries relevant to metric spaces, $b$-metric spaces, ultrametric spaces, and distance spaces with power triangle functions. Notably, several new and interesting findings emerge in the context of weak and partial contractions. |
| title | Fixed point theorems for weak, partial, Bianchini and Chatterjea-Bianchini contractions in semimetric spaces with triangle functions |
| topic | General Topology Primary 47H10, Secondary 47H09 |
| url | https://arxiv.org/abs/2501.00392 |