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

Volume 11, Issue 10, pp 1161--1170
Publication Date: July 15, 2018 Submission Date: August 13, 2017 Revision Date: January 06, 2018 Accteptance Date: January 11, 2018
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### 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.

### Share and Cite

##### ISRP Style

H. M. Srivastava, Ekrem Savaş, Richard F. Patterson, Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 10, 1161--1170

##### AMA Style

Srivastava H. M., Savaş Ekrem, Patterson Richard F., Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions. J. Nonlinear Sci. Appl. (2018); 11(10):1161--1170

##### Chicago/Turabian Style

Srivastava, H. M., Savaş, Ekrem, Patterson, Richard F.. "Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions." Journal of Nonlinear Sciences and Applications, 11, no. 10 (2018): 1161--1170

### Keywords

• Ideals and filters
• $\mathcal{I}$-statistical convergence
• $I_{\lambda}$-statistical convergence
• $\lambda$-statistical convergence
• de la Vallée Poussin method

•  40H05
•  40C05

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