Discontinuity at the fixed point in suprametric spaces
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| Format: | Preprint |
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2026
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| _version_ | 1866909023201132544 |
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| author | Fabiano, Nicola Barootkoob, Sedigheh Lakzian, Hossein |
| author_facet | Fabiano, Nicola Barootkoob, Sedigheh Lakzian, Hossein |
| contents | The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to generate a fixed point on a complete suprametric spaces but do not force the mapping to be continuous at the fixed point, and it can be replaced by relatively weaker conditions of $k$-continuity or $T$-orbitally lower semi-continuous. On this way a new and distinct solution to the open problem of Rhoades (Contemp Math 72:233-245,1988) is found. In sequel, we will prove some fixed point results in the setting suprametric spaces which are generalizations of the results regarding Sehgal, Ćirić and Fisher's quasi-contraction. Some examples and application will be approved our results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_06694 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discontinuity at the fixed point in suprametric spaces Fabiano, Nicola Barootkoob, Sedigheh Lakzian, Hossein General Mathematics Primary 47H10, Secondary 47H09 The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to generate a fixed point on a complete suprametric spaces but do not force the mapping to be continuous at the fixed point, and it can be replaced by relatively weaker conditions of $k$-continuity or $T$-orbitally lower semi-continuous. On this way a new and distinct solution to the open problem of Rhoades (Contemp Math 72:233-245,1988) is found. In sequel, we will prove some fixed point results in the setting suprametric spaces which are generalizations of the results regarding Sehgal, Ćirić and Fisher's quasi-contraction. Some examples and application will be approved our results. |
| title | Discontinuity at the fixed point in suprametric spaces |
| topic | General Mathematics Primary 47H10, Secondary 47H09 |
| url | https://arxiv.org/abs/2605.06694 |