S. S. Bhatia

Multiple sequences of fuzzy numbers and their statistical convergence

PurposeThe purpose of this paper is to extend a generalized convergence method, namely, statistical convergence to sequences of fuzzy numbers of multiplicity greater than two.MethodsWe use analytic method to obtain our results.ResultsCertain theorems on statistical convergence of real double sequences obtained by Savaş et al. and Móricz are also extended to multiple sequences of fuzzy numbers. Finally, we define Cesàro summable and strongly p-Cesàro summable multiple sequences of fuzzy numbers and obtained their relations with statistical convergence.ConclusionsAlthough, we prove our results only for triple sequences, but all these results remain true for d-multiple sequences as well.

Lacunary statistical limit and cluster points of generalized difference sequences of fuzzy numbers

The aim of present work is to introduce and study lacunary statistical limit and lacunary statistical cluster points for generalized difference sequences of fuzzy numbers. Some inclusion relations among the sets of ordinary limit points, statistical limit points, statistical cluster points, lacunary statistical limit points, and lacunary statistical cluster points for these type of sequences are obtained.

Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

The main objective of this paper is to introduce a new kind of sequence spaces by combining the concepts of modulus function, invariant means, difference sequences, and ideal convergence. We also examine some topological properties of the resulting sequence spaces. Further, we introduce a new concept of -convergence and obtain a condition under which this convergence coincides with above-mentioned sequence spaces.