Consider the following maps from the closed unit diskD = {(x, y) E R? : x² + y² < 1} in R2 to itself:%3Df(r. y) = ()g(x, y):%3Dh(x, y) = (xy, y)%3DWhich maps have exactly one fixed point in D?Only f and g.O Only g and h.Only h and f.All of f, g, and h.

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Answered: Consider the following maps from the…

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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Consider the following maps from the closed unit disk D = {(x, y) E R? : x? + y < 1} in R? to itself: %3D f(x. ) = () g(x, y) = %3D h(x, y) = (xy, y) %3D Which maps have exactly one fixed point in D? Only f and g. O Only g and h. Only h and f. All of f, g, and h.