Question

Every continuous function.....satisfy a lipschitz condition on a rectangle.a)May b)must c)May not d)None of these ​

Answer 1

Every continuous function must satisfy a Lipschitz condition on a rectangle.

Lipschitz continuity implies uniform continuity. Thus, every continuous function must satisfy a Lipschitz condition on a rectangle.

The Lipschitz continuity refers to a function's modulus of continuity bound. The Lipschitz condition is satisfied by a function f:[a,b]→R if there exists a constant M such that:

|f(x)-f'(x)| ≤ M |x-x'| , for every x, x'∈ [a, b]

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