In this paper, we study the concept of statistical convergence for double sequences on $ L- $fuzzy normed spaces. Then we give a useful characterization on the statistical convergence of double sequences with respect to their convergence in the classical sense and we illustrate that our method of convergence is weaker than the usual convergence for double sequences on $ L- $fuzzy normed spaces.
Citation: Reha Yapalı, Utku Gürdal. Pringsheim and statistical convergence for double sequences on $ L- $fuzzy normed space[J]. AIMS Mathematics, 2021, 6(12): 13726-13733. doi: 10.3934/math.2021796
In this paper, we study the concept of statistical convergence for double sequences on $ L- $fuzzy normed spaces. Then we give a useful characterization on the statistical convergence of double sequences with respect to their convergence in the classical sense and we illustrate that our method of convergence is weaker than the usual convergence for double sequences on $ L- $fuzzy normed spaces.
[1] | K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. |
[2] | O. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223–231. doi: 10.1016/j.jmaa.2003.08.004 |
[3] | J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145–174. |
[4] | B. Hazarika, A. Alotaibi, S. A. Mohiuddine, Statistical convergence in measure for double sequences of fuzzyvalued functions, Soft Comput., 24 (2020), 6613–6622. doi: 10.1007/s00500-020-04805-y |
[5] | S. Karakuş, K. Demirci, O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Soliton. Fract., 35 (2008), 763–769. doi: 10.1016/j.chaos.2006.05.046 |
[6] | F. Lael, K. Nourouzi, Some results on the $IF-$normed spaces, Chaos Soliton. Fract., 37 (2008), 931–939. doi: 10.1016/j.chaos.2006.10.019 |
[7] | S. A. Mohiuddine, Q. M. Danish Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Soliton. Fract., 42 (2009), 1731–1737. doi: 10.1016/j.chaos.2009.03.086 |
[8] | S. A. Mohiuddine, B. Hazarika, A. Alotaibi, On statistical convergence of double sequences of fuzzy valued functions, J. Intell. Fuzzy Sys., 32 (2017), 4331–4342. doi: 10.3233/JIFS-16974 |
[9] | M. Mursaleen, S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math., 233 (2009), 142–149. doi: 10.1016/j.cam.2009.07.005 |
[10] | M. Mursaleen, S. A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos Soliton. Fract., 41 (2009), 2414–2421. doi: 10.1016/j.chaos.2008.09.018 |
[11] | M. Mursaleen, S. A. Mohiuddine, H. H. E. Osama, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603–611. doi: 10.1016/j.camwa.2009.11.002 |
[12] | M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223–231. doi: 10.1016/j.jmaa.2003.08.004 |
[13] | J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Soliton. Fract., 22 (2004), 1039–1046. doi: 10.1016/j.chaos.2004.02.051 |
[14] | R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Soliton. Fract., 27 (2006), 331–344. doi: 10.1016/j.chaos.2005.03.019 |
[15] | R. Saadati, C. Park, Non-Archimedean L-fuzzy normed spaces and stability of functional equations, Comput. Math. Appl., 60 (2010), 2488–2496. doi: 10.1016/j.camwa.2010.08.055 |
[16] | R. Saadati, A. Razani, H. Adibi, A common fixed point theorem in $L-$fuzzy metric spaces, Chaos Soliton. Fract., 33 (2007), 358–363. doi: 10.1016/j.chaos.2006.01.023 |