Generalizations of Dini's Theorem under Weakened Monotonicity Conditions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910977501429760 |
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| author | Khatiwada, Riwaj |
| author_facet | Khatiwada, Riwaj |
| contents | Dini's Theorem guarantees that a monotone sequence of continuous functions converges pointwise on a compact interval to a continuous limit that converges uniformly. In this paper, we establish new theorems generalizing Dini's result by replacing the restrictive monotonicity assumption with more flexible conditions like equicontinuity, convexity, and controlled variation hypotheses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizations of Dini's Theorem under Weakened Monotonicity Conditions Khatiwada, Riwaj General Mathematics 03F60 Dini's Theorem guarantees that a monotone sequence of continuous functions converges pointwise on a compact interval to a continuous limit that converges uniformly. In this paper, we establish new theorems generalizing Dini's result by replacing the restrictive monotonicity assumption with more flexible conditions like equicontinuity, convexity, and controlled variation hypotheses. |
| title | Generalizations of Dini's Theorem under Weakened Monotonicity Conditions |
| topic | General Mathematics 03F60 |
| url | https://arxiv.org/abs/2506.00013 |