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New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function


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1 Department of Mathematics, National Institute of Technology, Silchar, Assam, India
     

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In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and suffcient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesaro summability.

Keywords

Triple Sequence of Fuzzy Numbers, Statistical Convergence, Statistically Pre-Cauchy Triple Sequence, Orlicz Function, Cesaro Summability.
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  • New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function

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Authors

Sangita Saha
Department of Mathematics, National Institute of Technology, Silchar, Assam, India
Santanu Roy
Department of Mathematics, National Institute of Technology, Silchar, Assam, India

Abstract


In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and suffcient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesaro summability.

Keywords


Triple Sequence of Fuzzy Numbers, Statistical Convergence, Statistically Pre-Cauchy Triple Sequence, Orlicz Function, Cesaro Summability.

References