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

Volume 11, Issue 10, pp 1161--1170 http://dx.doi.org/10.22436/jnsa.011.10.05 Publication Date: July 15, 2018       Article History

Authors

H. M. Srivastava - University of Victoria, Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada \(\&\) Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China, Victoria, British Columbia V8W 3R4, Canada. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China. Ekrem Savaş - department of Mathematics, Istanbul Ticaret (Commerce) University, Sutluce (Beyglu), TR-34672 Uskudar-Istanbul, Turkey. Richard F. Patterson - Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida 32224, U. S. A..


Abstract

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.


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