De termine an inter val Ca,b] on which figed pointiteration wil1 Con verge, for the equatron X= x2+1 3. TALSO, Use Theoreml2-3) to Show that gles= +1 has unique fixed point on Ca,b]. 3.
De termine an inter val Ca,b] on which figed pointiteration wil1 Con verge, for the equatron X= x2+1 3. TALSO, Use Theoreml2-3) to Show that gles= +1 has unique fixed point on Ca,b]. 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The following theorem gives sufficient conditions for the existence and uniqueness of a fixed
point.
Theorem 2.3: (i) If geTla, b] and g(x) E [a, b] for all xE [a, b), then g has at least
one fixed point in la, b).
(iiyIf, in addition, g(x) exists on (a, b) and a positive constant k <1 exists with
Paitit
lý (x) sk, for all xe (a,b).
then there is exactly one fixed point in [a, bj. (See Figure 2.4.)
Figure 2.4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F506bbca2-1e7d-45fa-87c2-523889971cdd%2F5675249c-f9b8-4cc2-8d32-4ce5d4e28862%2F06saq1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following theorem gives sufficient conditions for the existence and uniqueness of a fixed
point.
Theorem 2.3: (i) If geTla, b] and g(x) E [a, b] for all xE [a, b), then g has at least
one fixed point in la, b).
(iiyIf, in addition, g(x) exists on (a, b) and a positive constant k <1 exists with
Paitit
lý (x) sk, for all xe (a,b).
then there is exactly one fixed point in [a, bj. (See Figure 2.4.)
Figure 2.4
![De termine an inter Val Ca,b] on which figed pointiteration wil1 -
Con Verge, for the equation
to Show that glxs= X1 has unique fixed point on Ca,b).
X= x2+1
ALSO, Use Theoreml2-3)
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F506bbca2-1e7d-45fa-87c2-523889971cdd%2F5675249c-f9b8-4cc2-8d32-4ce5d4e28862%2F9clpw4f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:De termine an inter Val Ca,b] on which figed pointiteration wil1 -
Con Verge, for the equation
to Show that glxs= X1 has unique fixed point on Ca,b).
X= x2+1
ALSO, Use Theoreml2-3)
3.
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