query: $d(Tx, Ty) < d(x, y)$ does not guarantee existence of fixed point.
positive_passages.docid: 27948
positive_passages.text: show that a function $A$ such that $ \rho (Ax,Ay)< \rho (x,y) $ $ \forall x\neq y $ not necessary has a fix point $ (Ax\neq x \space \forall x )$
negative_passages.docid: 89462
negative_passages.text: Convergence of the fixed point iteration for sin(x)
negative_passages.docid: 4538
negative_passages.text: Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
negative_passages.docid: 45025
negative_passages.text: IID Random Variables that are not constant can't converge almost surely
negative_passages.docid: 14509
negative_passages.text: Contraction Map on Compact Normed Space has a Fixed Point
negative_passages.docid: 148266
negative_passages.text: Let $f:X\to X $ be continuous. Does $f $ have a fixed point when $X=[0,1)$ or $X=(0,1) $?
negative_passages.docid: 11017
negative_passages.text: Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
negative_passages.docid: 54222
negative_passages.text: Prove the map has a fixed point
negative_passages.docid: 17234
negative_passages.text: Show that a continuous function has a fixed point
negative_passages.docid: 60746
negative_passages.text: Simply connected does not imply contractible. Is there a nice counter example in $R^2$?
negative_passages.docid: 105960
negative_passages.text: Counterexamples to Brouwer's fixed point theorem for the closed unit ball in Banach space
negative_passages.docid: 77464
negative_passages.text: Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
negative_passages.docid: 20568
negative_passages.text: Does the following have a solution for f(x,y)?
negative_passages.docid: 82280
negative_passages.text: Problem about continuous functions and the intermediate value theorem
negative_passages.docid: 123132
negative_passages.text: Counterexample for a non-measurable function?
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 74352
negative_passages.text: A weak version of Markov-Kakutani fixed point theorem