Real Analysis: Contractions and Picard’s Fixed-point Theorem. Lect. 18.

Real Analysis:
Metric Spaces: Contraction on Metric Space.
Picard’s Fixed-point Theorem: statement and proof.
In the statement of the Picard’s Fixed-point Theorem, at time stamp 8:54, please read as Let M be a “complete “ metric space.
Link for playlist of Metric Spaces:
• Real Analysis: Metric ...
The book followed is
Richard R Goldberg: Methods of Real Analysis
Link for Handwritten notes: (send a request mail, I will share it with you)
1. Limits in Metric Spaces.
drive.google.c...
2. Continuous Functions on Metric Spaces.
drive.google.c...
3. Connectedness, Completeness and Compactness. Pages 1 to 19.
drive.google.c...
4. Connectedness, Completeness and Compactness. Pages 20 to 25.
drive.google.c...

[@evilfairy7460]

I really have no words😭 Today i had an exam but i couldn't understand this theorem. Thank God I've found this video. You're really doing a great job sir, even though the views are low keep uploading the videos sir. I wish I could get a teacher like you sir

[@BScMathematicsDrSSPhulsagar]

Thank you for your complements.

[@sahanas4575]

Thank you for all your videos sir... I'm very excited to learn real analysis after watching all your lectures. With a week I have real exam I wish I could found your channel before😿

[@BScMathematicsDrSSPhulsagar]

You are welcome. Best wishes for your study and exam.

[@algorithmo134]

Hi Sir, you should consider doing a playlist for each real analysis topic which covers everything in the book RR Goldberg. You are excellent in teaching students. Very clear concepts! God bless!

[@BScMathematicsDrSSPhulsagar]

Okay. I will try. Thank you.

[@mahalakshmig5232]

Sir can you explain regarding cauchy criterion for uniform convergence?

[@BScMathematicsDrSSPhulsagar]

No. It is not included in our university’s syllabus.

[@mahalakshmig5232]

Kk sir

[@viji.d927]

Sir T suffix x or Tx?

[@BScMathematicsDrSSPhulsagar]

We are writing(to simplify notation)
Tx instead of T(x).
It is Tx and not T suffix x.

[@jaganraj_r]

8:54 complete metric space

[@BScMathematicsDrSSPhulsagar]

Yes. In the statement of the theorem please read as M be a complete metric space. Thank you for suggesting the correction.