The Convergence Behavior of a One-Parameter Family

Let , for . For any , . Moreover:
1. If , then is strictly increasing.
2. If , then is strictly decreasing.
3. If , then has exactly one local minimum and it is the absolute minimum.

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Reference: C. X. Kang and E. Yi, "The convergence behavior of ," The College Mathematics Journal, 38(5), 2007 pp. 385–386.

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