Question

question number 26

M u Dy - 4211 - ) maps the interval [0, 1] into itself and is not a contraction. Prove that it has a fixed point. Why does this not contradict the Contractive Mapping Theorem? (26) If the method of functional iteration is used on the function f(1) = (1 + )- starting at Io = 7, will the resulting sequence converge? If so, what is the limit? Establish your answers rigorously. (27. Prove or disprove: If F: R ſa, b] and if F is contractive on In Althen i

Answer 1

fox) = 1 | +227 # amarafton) 20-7 {By Iterative method) - 24 = $1262 - (lt tu?) (144) * = }50) = (002) QOL a fine (1710.0172) = 0.49995 pizo fue) 11174014945)+)?? 30.40002 my fing) - 744.000274) c.0.4310 3 cs) Scanned with his firme) Scanned with Camscanitet

- sitt 10.4.3403)) 120.42066 h = fins) = +LOvje:26) ?) 2 30.42452 ! . I = *(1+/0.42452)27) =0,42365 fing) 2 (i+10.42365)) = 0.42392 ag - fline) 2 H+48.4239272) CamScanner = 0.42383

240 643622 +10.42382)2.) : 0.42386 So, the function starting at no=7 ffu) = + (1+22) will result in Also flu) = 11422522 cse (1722) & If loll sequence converges Scanned with CamScanner