Question

Define bounded variation for a function $\phi$. show that if $\phi$ is of bounded variation then it is bounded also. Whether converse holds? Justify.

Answer 1

Bounded variation. In mathematical analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense.

Answer 2

Step-by-step explanation:

➡️Functions of bounded variations form important transition between absolute continuous and singular functions. With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations.