Example of a nowhere differentiable contraction mapping
$begingroup$
The Weierstrass function https://en.wikipedia.org/wiki/Weierstrass_function
is a pathological example of a continuous nowhere differentiable function.. Since a conttaction mapping is necessarily Lipschitz continuous (which is a stronger form of continuity), I was wondering if there exists a (pathological) example of a contraction mapping that is nowhere differentiable
continuity lipschitz-functions contraction-operator
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
$endgroup$
add a comment |
$begingroup$
The Weierstrass function https://en.wikipedia.org/wiki/Weierstrass_function
is a pathological example of a continuous nowhere differentiable function.. Since a conttaction mapping is necessarily Lipschitz continuous (which is a stronger form of continuity), I was wondering if there exists a (pathological) example of a contraction mapping that is nowhere differentiable
continuity lipschitz-functions contraction-operator
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
$endgroup$
add a comment |
$begingroup$
The Weierstrass function https://en.wikipedia.org/wiki/Weierstrass_function
is a pathological example of a continuous nowhere differentiable function.. Since a conttaction mapping is necessarily Lipschitz continuous (which is a stronger form of continuity), I was wondering if there exists a (pathological) example of a contraction mapping that is nowhere differentiable
continuity lipschitz-functions contraction-operator
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
$endgroup$
The Weierstrass function https://en.wikipedia.org/wiki/Weierstrass_function
is a pathological example of a continuous nowhere differentiable function.. Since a conttaction mapping is necessarily Lipschitz continuous (which is a stronger form of continuity), I was wondering if there exists a (pathological) example of a contraction mapping that is nowhere differentiable
continuity lipschitz-functions contraction-operator
continuity lipschitz-functions contraction-operator
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
asked Dec 29 '18 at 7:39
Somo S.Somo S.
1284
1284
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No, by Rademacher's theorem a Lipschitz function $Bbb R^ntoBbb R^n$ is differentiable almost everywhere. A proof of this result can be found, for example, in Emmanuele DiBenedetto's Real Analysis, Theorem 21.1.
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3055629%2fexample-of-a-nowhere-differentiable-contraction-mapping%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
No, by Rademacher's theorem a Lipschitz function $Bbb R^ntoBbb R^n$ is differentiable almost everywhere. A proof of this result can be found, for example, in Emmanuele DiBenedetto's Real Analysis, Theorem 21.1.
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
$endgroup$
add a comment |
$begingroup$
No, by Rademacher's theorem a Lipschitz function $Bbb R^ntoBbb R^n$ is differentiable almost everywhere. A proof of this result can be found, for example, in Emmanuele DiBenedetto's Real Analysis, Theorem 21.1.
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
$endgroup$
add a comment |
$begingroup$
No, by Rademacher's theorem a Lipschitz function $Bbb R^ntoBbb R^n$ is differentiable almost everywhere. A proof of this result can be found, for example, in Emmanuele DiBenedetto's Real Analysis, Theorem 21.1.
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
$endgroup$
No, by Rademacher's theorem a Lipschitz function $Bbb R^ntoBbb R^n$ is differentiable almost everywhere. A proof of this result can be found, for example, in Emmanuele DiBenedetto's Real Analysis, Theorem 21.1.
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
edited Dec 29 '18 at 13:03
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
answered Dec 29 '18 at 9:52
Alessandro CodenottiAlessandro Codenotti
3,83011839
3,83011839
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3055629%2fexample-of-a-nowhere-differentiable-contraction-mapping%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
