Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

Ömer Kişi and Hijaz Ahmad

Journal of Mathematics, 2021, vol. 2021, 1-12

Abstract: Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α-level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6655630

DOI: 10.1155/2021/6655630

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