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Why is $x=4$ as a fixed point of a map $\sqrt{2}^{x}$ unstable?

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#dynamical-systems #exponentiation #fixed-point-theorems #power-towers
50
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Prove that there exists at least on fixed point of T. Hint consider the map $T_k = (1-\frac{1}{k})T$

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#real-analysis #fixed-point-theorems
130
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Is the function is contraction? How to find fixed point?

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#functional-analysis #functions #fixed-point-theorems #contraction-operator
175
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Proving the error estimate of a contraction in Banach space via induction

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#functional-analysis #banach-spaces #fixed-point-theorems #contraction-operator
188
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System of equations $a(1 - b^2) = b(1 -c^2) = c(1 -d^2) = d(1 - a^2)$

Published on
#calculus #systems-of-equations #fixed-point-theorems #fixed-points
383
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Is Banach fixed point theorem a necessary and sufficient condition for the existence of a fixed point

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#functional-analysis #banach-spaces #machine-learning #fixed-point-theorems
161
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Reverse fixed point conclusion

Published on
#real-analysis #metric-spaces #fixed-point-theorems
50
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Is there a holomorphic diffeomorphism of $\mathbb{C}P^{2n+1}$ without fixed point?

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#complex-analysis #fixed-point-theorems #projective-space
1.1k
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Showing a function is Frechet Differentiable？

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#calculus #real-analysis #banach-spaces #fixed-point-theorems #frechet-derivative
294
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Find good starting candidates for Newton-Raphson knowing one of the solutions of a parametrized system of nonlinear equations

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#real-analysis #numerical-methods #fixed-point-theorems #newton-raphson
423
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$f(a)-f(b)$ is rational iff $f(a-b) $ is rational

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#real-analysis #continuity #functional-equations #rational-numbers #fixed-point-theorems
60
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Root of a plynomial in (0,1)

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#real-analysis #polynomials #binomial-coefficients #fixed-point-theorems #binomial-distribution
80
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If $g:X \to [0,\infty)$ is defined by $g(x)=d(x,f(x))$, prove that $g$ is uniformly continuous on $X$.

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#real-analysis #uniform-continuity #fixed-point-theorems #fixed-points
558
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Picard's method does not solve first order differential equation?

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#ordinary-differential-equations #fixed-point-theorems #contraction-operator #picard-scheme
321
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How to find g(x) and aux function h(x) when doing fixed point interation?

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#fixed-point-theorems #fixed-points

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