Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions

The aim of this paper is to introduce and investigate some new definitions which are interrelated to the notions of asymptotically Iλ-statistical equivalence of multiple L and strongly Iλ-asymptotic equivalence of multiple L. Indeed, instead of sequences, the authors make use of two nonnegative real-valued Lebesgue measurable functions in the open interval (1,1) and present a series of inclusion theorems associated with these new definitions. Furthermore, in connection with one of the main results which are proven in this paper, a closely-related open problem is posed for the interested reader.