If f is concave upward on [a,b], then is average value of f more than f(a+b/2)?
2848
Convex integral inequality
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
140383
Concave implies subadditive
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
29325
Maximum Proof (Average?)
104263
How to show that $f'(x)<2f(x)$
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
112404
Eliminating discontinuities for increasing function
90892
Is a function increasing if the derivative is positive except at one point of an interval?
138490
An inequality with a weird condition
99431
Increasing functions are Baire one
76790
Condition to guarantee $f=0$ on $[a,b]$
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
73553
How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?
67738
Mean Value theorem problem?(inequality)
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.