Question

All solutions of $f\left(\frac{1}{x}\right)=\sqrt{x}f(x)$

score 120 · Answer 1 · 2020-03-16 17:23:52

120

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All solutions of $f\left(\frac{1}{x}\right)=\sqrt{x}f(x)$

Published on 16 Mar 2020 - 17:23

score 1.2k · Answer 2 · 2020-03-17 17:12:12

1.2k

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how can I find out the general solution of Jensen's functional equation?

Published on 17 Mar 2020 - 17:12

score 90 · Answer 3 · 2020-03-19 13:02:52

90

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A continuous function $f:[1, \infty)\to \mathbb{R}$ such that $2xf(x^2)=(x+1)f(x)$, $\forall x\ge 1$

Published on 19 Mar 2020 - 13:02

score 116 · Answer 4 · 2020-03-20 01:17:39

116

Views

Cyclic function in functional equation

Published on 20 Mar 2020 - 1:17

score 105 · Answer 5 · 2020-03-21 18:25:45

105

Views

Which functions $f$ satisfies the equation $f’(x)=\dfrac{1}{x}\left(f(\sqrt{1-x^2})- f(x)\right)$?

Published on 21 Mar 2020 - 18:25

score 778 · Answer 6 · 2020-03-22 12:56:39

778

Views

How to find a function $f$ that satisfy the equation $f(x)=f(x-1)+x^2$

Published on 22 Mar 2020 - 12:56

score 57 · Answer 7 · 2020-03-22 16:59:33

57

Views

Is there a continuous function g that satisfies $2sg'(s)=g(1-s) - g(s)$

Published on 22 Mar 2020 - 16:59

score 119 · Answer 8 · 2020-03-23 12:27:43

119

Views

Solving multivariable functional equation

Published on 23 Mar 2020 - 12:27

score 36 · Answer 9 · 2020-03-24 20:25:47

36

Views

A functional equation on continuous and monotone functions

Published on 24 Mar 2020 - 20:25

score 80 · Answer 10 · 2020-03-25 09:31:36

80

Views

Which polynomial functions can satisfy $f(x)\cdot f({1\over x}) = f(x) + f({1\over x})$?

Published on 25 Mar 2020 - 9:31

score 31 · Answer 11 · 2020-03-26 14:33:03

31

Views

real-valued functional equations on a closed interval

Published on 26 Mar 2020 - 14:33

score 33 · Answer 12 · 2020-03-26 19:47:13

33

Views

how to solve the equation $sg’(s) + g(s) = ag(ks)$

Published on 26 Mar 2020 - 19:47

score 38 · Answer 13 · 2026-03-25 13:51:35

38

Views

Considering this constraint, determine the real function $f$

Published on 25 Mar 2026 - 13:51

score 77 · Answer 14 · 2020-03-27 10:22:12

77

Views

Functional question $f(x+y)=f(x)+f(y)+xy$ involving derivation

Published on 27 Mar 2020 - 10:22

score 57 · Answer 15 · 2026-03-29 16:56:05

57

Views

Dilation operator on $(0,\infty)$ "not injective"

Published on 29 Mar 2026 - 16:56

List Question

All solutions of $f\left(\frac{1}{x}\right)=\sqrt{x}f(x)$

how can I find out the general solution of Jensen's functional equation?

A continuous function $f:[1, \infty)\to \mathbb{R}$ such that $2xf(x^2)=(x+1)f(x)$, $\forall x\ge 1$

Cyclic function in functional equation

Which functions $f$ satisfies the equation $f’(x)=\dfrac{1}{x}\left(f(\sqrt{1-x^2})- f(x)\right)$?

How to find a function $f$ that satisfy the equation $f(x)=f(x-1)+x^2$

Is there a continuous function g that satisfies $2sg'(s)=g(1-s) - g(s)$

Solving multivariable functional equation

A functional equation on continuous and monotone functions

Which polynomial functions can satisfy $f(x)\cdot f({1\over x}) = f(x) + f({1\over x})$?

real-valued functional equations on a closed interval

how to solve the equation $sg’(s) + g(s) = ag(ks)$

Considering this constraint, determine the real function $f$

Functional question $f(x+y)=f(x)+f(y)+xy$ involving derivation

Dilation operator on $(0,\infty)$ "not injective"

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