A normed space X is said to be strictly convex if for x # y in X with |||| = 1 = ||yl|, we have ||x+y|| < 2. This says that the mid-point (x + y)/2 of two distinct points a and y on the unit sphere of X does not lie on the unit sphere of X, but it lies in the open unit ball U(0, 1) of X. In particular, no line segment lies on the unit sphere. Request explain marked portion

A normed space X is said to be strictly convex if for x # y in X with |||| = 1 = ||yl|, we have ||x+y|| < 2. This says that the mid-point (x + y)/2 of two distinct points a and y on the unit sphere of X does not lie on the unit sphere of X, but it lies in the open unit ball U(0, 1) of X. In particular, no line segment lies on the unit sphere. Request explain marked portion

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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