Approximation of integrable functions based on \phi -transform

Let \(E\) be a bounded subset of real line which contains its infimum and supremum. In this paper, we have defined the \(\phi -\) transform and its inverse, where \(\phi \) is a function from \(E\) into \((0,1]\) . We will have shown that real-valued integrable functions on \(a, b]\) and real-valued continuous functions on \(E\) can be approximated by this transformation with an arbitrary precision.