TY - JOUR AU - Srivastava, H. M. AU - Savaş, Ekrem AU - Patterson, Richard F. PY - 2018 TI - Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions JO - Journal of Nonlinear Sciences and Applications SP - 1161--1170 VL - 11 IS - 10 AB - The aim of this paper is to introduce and investigate some new definitions which are interrelated to the notions of asymptotically \( I_\lambda\)-statistical equivalence of multiple \(L\) and strongly \(I_\lambda\)-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 \((1,\infty)\) 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.10.05 DO - 10.22436/jnsa.011.10.05 ID - Srivastava2018 ER -