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  • Member for 9 years, 7 months
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  • India
22 votes
4 answers
12k views

Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?

22 votes
4 answers
5k views

If $f:[0,\infty)\to [0,\infty)$ and $f(x+y)=f(x)+f(y)$ then prove that $f(x)=ax$

11 votes
3 answers
4k views

If $ \int_0^{\pi}f(x)\cos(nx)\,dx=0$ for all $n$ then prove that $f\equiv 0$

10 votes
8 answers
3k views

Solve the congruence relation $x^n\equiv 2\pmod {13}$.

8 votes
3 answers
1k views

Find dimension of the space of all linear maps from $\Bbb R^{13}$ to $\mathbb R^{31}$

8 votes
5 answers
10k views

If $A^2 =0$ then possible rank of $A$

8 votes
2 answers
2k views

Existence of Holomorphic function (Application of Schwarz-Lemma)

8 votes
1 answer
3k views

Does there exist an analytic function s.t. $f\left(\frac{1}{n}\right)=2^{-n}.$

7 votes
2 answers
4k views

If $f$ is continuous & $\lim_{|x|\to {\infty}}f(x)=0$ then $f$ is uniformly continuous or NOT?

7 votes
3 answers
1k views

Number of solutions for IVP $\frac{dy}{dx}=3y^{{2}/{3}}$

7 votes
1 answer
6k views

Dimension of set of all homogeneous polynomial of degree $d$ in $n$-variables over a field $F$

7 votes
1 answer
1k views

If $z\mapsto f(z)^n$ is analytic then $f$ is analytic

7 votes
2 answers
3k views

Harmonic conjugate of $\ln|z|$ in $\mathbb C \setminus \{0\}$

7 votes
2 answers
3k views

Basis of $C[a,b]$

7 votes
3 answers
158 views

Solve the Volterra type integral equation

7 votes
1 answer
391 views

Find all entire function $f$ such that $\lim_{z\to \infty}\left|\frac{f(z)}{z}\right|=0$

7 votes
1 answer
2k views

$P$ is a monic polynomial of degree $n$ , then which are correct?

6 votes
3 answers
199 views

Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$

6 votes
3 answers
194 views

Continuity and uniform continuity of $f(x)$ over $\mathbb Q$

6 votes
3 answers
1k views

Does there exist an analytic function $f$ such satisfying the following three conditions?

5 votes
2 answers
370 views

Question about open mapping theorem

5 votes
1 answer
327 views

Are there exists an analytic function satisfying the following condition

5 votes
2 answers
147 views

Prove that $\{n^2f\left(\frac{1}{n}\right)\}$ is bounded.

5 votes
3 answers
790 views

Uniform convergence with two sequences of functions

5 votes
1 answer
11k views

$A$ and $B$ be two orthogonal matrices with $|A|+|B|=0$. Then prove that $(A+B)$ is singular [duplicate]

5 votes
1 answer
178 views

Evaluate the integration $\int_{|z|=100}f(z)\,dz$

5 votes
2 answers
858 views

$S$ is a $3\times 3$ real matrices. Then $S$ contains which matrices

5 votes
1 answer
1k views

Number of solutions in a field of order $32$ [duplicate]

5 votes
1 answer
2k views

Variation of argument of a complex function

5 votes
1 answer
1k views

A continuous onto function from $[0,1)$ to $(-1,1)$

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