Let X be the set of all continuous functions defined on the interval [a,b]. Let d: X × X →R be a function defined as follows d(f,8)=f[f(x)-8(x)| dx ¥f•g eX Show that (X,d )is a metric space
Let X be the set of all continuous functions defined on the interval [a,b]. Let d: X × X →R be a function defined as follows d(f,8)=f[f(x)-8(x)| dx ¥f•g eX Show that (X,d )is a metric space
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Help4
![Let X be the set of all continuous functions defined on the interval
[a,b]. Let d: X x X R be a function defined as follows
d(S.8) = j[/(x)- «(x) dx V.g eX
Show that (X,d)is a metric space
Remark: f and g are continuous functions so f - g| is continuous.
Remark: Since integral of a continuous function over a closed and
bounded interval is always finite, therefore d(f.g) exists for any
f.g e X. Thus d is a well-defined function](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf185105-2501-43b5-9e3a-552ae94f0481%2F718393ca-178d-4903-9181-cd103c527d1c%2Fa4237jd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X be the set of all continuous functions defined on the interval
[a,b]. Let d: X x X R be a function defined as follows
d(S.8) = j[/(x)- «(x) dx V.g eX
Show that (X,d)is a metric space
Remark: f and g are continuous functions so f - g| is continuous.
Remark: Since integral of a continuous function over a closed and
bounded interval is always finite, therefore d(f.g) exists for any
f.g e X. Thus d is a well-defined function
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
