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

Srivastava, H. M. ¹ ; Savaş, Ekrem ² ; Patterson, Richard F. ³

¹ 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
² department of Mathematics, Istanbul Ticaret (Commerce) University, Sutluce (Beyglu), TR-34672 Uskudar-Istanbul, Turkey
³ Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida 32224, U. S. A.

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 10, p. 1161-1170.

Résumé

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.

Détail

DOI : 10.22436/jnsa.011.10.05

Classification : 40H05, 40C05
Keywords: Ideals and filters, \(\mathcal{I}\)-statistical convergence, \(I_{\lambda}\)-statistical convergence, \(\lambda\)-statistical convergence, de la Vallée Poussin method

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