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

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  • Ömer KiÅŸi
  • Hijaz Ahmad

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.

Suggested Citation

  • Ömer KiÅŸi & Hijaz Ahmad, 2021. "Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, March.
    • Handle: RePEc:hin:jjmath:6655630
    DOI: 10.1155/2021/6655630
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