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Proving functional space $B(A)$ as Banach space.

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#real-analysis #functional-analysis #supremum-and-infimum
265
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Find the supreme and infimum of the following set, $\left \{\dfrac{3n}{\sqrt{1+2n^2}}: n\in \Bbb N\right \}$.

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#supremum-and-infimum #upper-lower-bounds
66
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supremum and summation Inequality

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#sequences-and-series #functional-analysis #lp-spaces #supremum-and-infimum
171
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$\int f^{-1}$ when $f$ contains jump discontinuities

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#calculus #integration #supremum-and-infimum #inverse-function #riemann-sum
298
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Let $S$ be a bounded and nonempty subset of $\mathbb{R}^{+}$. Prove that $\sup(\frac{1}{S}) = \frac{1}{\inf S}, \inf S > 0$

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#real-analysis #supremum-and-infimum
87
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Proving that if a sequence $(a_n)$ is monotonic decreasing and $\lim a_n = l$, then $l=\inf \{a_n:n\in\mathbf{N}\}$

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#real-analysis #solution-verification #supremum-and-infimum
187
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What is the infimum over $x$ of the lagrangian function?

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#convex-analysis #convex-optimization #supremum-and-infimum #lagrange-multiplier #duality-theorems
37
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How to show the mapping from $x$ to its unique best approximation is continuous?

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#functional-analysis #analysis #supremum-and-infimum
59
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Taking supremum from integral

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#supremum-and-infimum #quantum-mechanics #greens-function
58
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How to prove the criteria for lower semicontinuity of a function at a point?

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#supremum-and-infimum #semicontinuous-functions
118
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Infimum and Supremum of a set 2^k

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#real-analysis #supremum-and-infimum
60
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Picard-Lindelöf to show whether $u'=u^2-u^3$ has unique solution on an interval

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#ordinary-differential-equations #continuity #supremum-and-infimum
117
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$f:R\to R$ has the property for $y\in R$, $\sup_{x\in R} [xy-f(x)]$ is finite. Then prove $\lim_{|x|\to\infty} \frac{f(x)}{|x|}=+\infty$

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#real-analysis #supremum-and-infimum
34
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limit of inf of a sequence

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#probability #probability-theory #supremum-and-infimum #limsup-and-liminf
66
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Why is $\sqrt{ab} = \inf_{\lambda>0} \frac{a}{2\lambda}+\frac{\lambda b}{2}$?

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#radicals #supremum-and-infimum

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