metric space is a set M together with a distance function p(z, y) tha (i) p(z,y) > 0 and (z,y)-0 if and only if y; (İİİ) plz, y) p(z, z) +pls, y) for all a, y,z in M. between elements r and y of the set M. The distance function must sa Let (M. p) be a metric space. A mapping T from M into M is called a contraction if for some constant a with 0 S a <1, and all r and y in M 3. Let С[0.1] denote the set of continuous functions f : [0, 1]-+ R with metric max If(t)--g(t) tejo.i Using 1.g in Co. I given by fe) 1 and g C(o.1 C0. 1] defined by 0 show that the mapping T: (Tx)(t) 1+r(s) ds is not a contraction mapping
metric space is a set M together with a distance function p(z, y) tha (i) p(z,y) > 0 and (z,y)-0 if and only if y; (İİİ) plz, y) p(z, z) +pls, y) for all a, y,z in M. between elements r and y of the set M. The distance function must sa Let (M. p) be a metric space. A mapping T from M into M is called a contraction if for some constant a with 0 S a <1, and all r and y in M 3. Let С[0.1] denote the set of continuous functions f : [0, 1]-+ R with metric max If(t)--g(t) tejo.i Using 1.g in Co. I given by fe) 1 and g C(o.1 C0. 1] defined by 0 show that the mapping T: (Tx)(t) 1+r(s) ds is not a contraction mapping
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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![metric space is a set M together with a distance function p(z, y) tha
(i) p(z,y) > 0 and (z,y)-0 if and only if y;
(İİİ) plz, y) p(z, z) +pls, y) for all a, y,z in M.
between elements r and y of the set M. The distance function must sa
Let (M. p) be a metric space. A mapping T from M into M is called a contraction if
for some constant a with 0
S a <1, and all r and y in M
3. Let С[0.1] denote the set of continuous functions f : [0, 1]-+ R with metric
max If(t)--g(t)
tejo.i
Using 1.g in Co. I given by fe) 1 and g
C(o.1 C0. 1] defined by
0 show that the mapping T:
(Tx)(t) 1+r(s) ds
is not a contraction mapping](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4aa5341f-3bcd-401e-8b0d-7704b9391f07%2Fc5606e6e-4526-4791-bab0-5a0e7ec68795%2Fobi26d.jpeg&w=3840&q=75)
Transcribed Image Text:metric space is a set M together with a distance function p(z, y) tha
(i) p(z,y) > 0 and (z,y)-0 if and only if y;
(İİİ) plz, y) p(z, z) +pls, y) for all a, y,z in M.
between elements r and y of the set M. The distance function must sa
Let (M. p) be a metric space. A mapping T from M into M is called a contraction if
for some constant a with 0
S a <1, and all r and y in M
3. Let С[0.1] denote the set of continuous functions f : [0, 1]-+ R with metric
max If(t)--g(t)
tejo.i
Using 1.g in Co. I given by fe) 1 and g
C(o.1 C0. 1] defined by
0 show that the mapping T:
(Tx)(t) 1+r(s) ds
is not a contraction mapping
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