9 Questions 134 Answers 0 Followers
Questions related from George Stoica
Let a ∈ ℝ and b > 0 be fixed. Find all functions f : [0, ∞) → ℝ satisfying the differential equation f'(x) = -a + b/f(x) for x > 0 and f(0) = 0.
22 January 2021 9,191 13 View
Let 0 < xn ↗ ∞ such that xn+1 - xn → 0 as n → ∞ . Then, for every 0 < c < 1, there exists a subsequence k(n) such that xk(n) - xn → c as n → ∞ . Is the problem true if c ≥ 1?
26 December 2020 3,862 45 View
I have some complicated hints and clues, but I think their solutions should be much simpler.
13 September 2020 6,765 4 View
Let T denote the circle group, that is, the multiplicative group of all complex numbers with absolute value 1. Let f : T → T be a (sequentially) continuous map, and such that f(z2 ) = f2 (z) for...
25 July 2020 2,182 3 View
If it makes easier, assume that f is continuous on [0,∞).
25 July 2020 2,970 3 View
For any given function f : [a, b] → R, there exists a sequence of polynomial functions converging to f at each point where f is continuous. (Note that we did not ask the convergence to be uniform).
25 July 2020 9,095 30 View
If the answer is yes, can one replace log n by another sequence that approaches ∞ faster than log n ?
22 July 2020 7,665 4 View
To avoid trivial solutions, assume that a and b are non-zero real numbers. My feeling is that, for certain values of a and b, there are no such functions.
14 July 2020 4,865 24 View
I was able to prove (only) that neither sequence has a finite limit; probably anyone saw that coming, but it does not answer the question in full. Am I missing something, or is this hard to get?...
04 July 2020 3,874 99 View