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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.23658 |
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| _version_ | 1866910248184315904 |
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| author | Petrov, Evgeniy |
| author_facet | Petrov, Evgeniy |
| contents | Let $(X,d)$ be a nonempty metric space and let $n\in \mathbb N^+$. We shall say that $T\colon X\to X$ is a graphic contraction of order $n$ if there exists $α\in (0,1)$ such that the inequality $$
d(T^n x,T^{2n}x) \leqslant αd(x,T^nx) $$ holds for all $x\in X$. In the case $n=1$ these mapping are known as graphic contractions and are well studied. In the present paper, we establish a theorem on the existence of periodic points for a graphic contraction of order $n$. Examples of such mappings having different properties are constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23658 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Periodic point theorem for generalized graphic contractions Petrov, Evgeniy General Topology 47H09, 47H10 Let $(X,d)$ be a nonempty metric space and let $n\in \mathbb N^+$. We shall say that $T\colon X\to X$ is a graphic contraction of order $n$ if there exists $α\in (0,1)$ such that the inequality $$ d(T^n x,T^{2n}x) \leqslant αd(x,T^nx) $$ holds for all $x\in X$. In the case $n=1$ these mapping are known as graphic contractions and are well studied. In the present paper, we establish a theorem on the existence of periodic points for a graphic contraction of order $n$. Examples of such mappings having different properties are constructed. |
| title | Periodic point theorem for generalized graphic contractions |
| topic | General Topology 47H09, 47H10 |
| url | https://arxiv.org/abs/2605.23658 |