Let (X, d) be a compact metric space and T: XX be a mapping thatsatisfiesd(Tr,Ty) < d(2,y)for all x, y EX such that xy. Prove that T has a unique fixed point.

What is Metric Space: Metric space is an abstract set in mathematics, particularly topology, with a…

Answered: Let (X, d) be a compact metric space…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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Let (X, d) be a compact metric space and T: XX be a mapping that satisfies d(Tr,Ty)