New theorems generalize Dini's theorem by using equicontinuity and convexity conditions, suggesting broader applications.
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.
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Riwaj Khatiwada (2025) studied this question.
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