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Year 2019, Volume: 7 Issue: 2, 405 - 409, 15.10.2019

Erdinç Dundar , Muhammed Recai Türkmen

Abstract

References

  • [1] Bag, T. and Samanta, S.K., Fixed point theorems in Felbin's type fuzzy normed linear spaces, J. Fuzzy Math. 16(1) (2008), 243-260.
  • [2] Bede, B. and Gal, S.G., Almost periodic fuzzy-number-valued functions, Fuzzy Sets Syst. 147(2004), 385-403.
  • [3] Das, P., Kostyrko, P., Wilczynski, W. and Malik, P., I and I*-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620.
  • [4] Das, P. and Malik, P., On extremal I-limit points of double sequences, Tatra Mt. Math. Publ. 40 (2008), 91-102.
  • [5] Diamond, P. and Kloeden, P., Metric Spaces of Fuzzy Sets-Theory and Applications, World Scienti c Publishing, Singapore (1994).
  • [6] Dündar, E. and Altay, B., I2-convergence and I2-Cauchy of double sequences, Acta Mathematica Scientia, 34(2) (2014), 343-353.
  • [7] Dündar, E. and Altay, B., On some properties of I2-convergence and I2-Cauchy of double sequences, Gen. Math. Notes, 7(1) (2011), 1-12.
  • [8] Dündar, E. and Talo,  O., I2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems, 10(3) (2013), 37-50
  • [9] Dündar, E. and Talo,  O., I2-Cauchy Double Sequences of Fuzzy Numbers, Gen. Math. Notes, 16(2) (2013), 103-114.
  • [10] Fang, J.-X. and Huang, H., On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets Systems, 147 (2004), 417-415.
  • [11] Fast, H., Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [12] Felbin, C., Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48(2) (1992), 239-248.
  • [13] Hazarika, B., On ideal convergent sequences in fuzzy normed linear spaces, Afrika Matematika, 25(4) (2013), 987-999.
  • [14] Hazarika, B. and Kumar, V., Fuzzy real valued I-convergent double sequences in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, 26 (2014), 2323-2332.
  • [15] Kostyrko, P., Salat, T. and Wilczynski, W., I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • [16] Kumar, V., On I and I*-convergence of double sequences, Math. Commun. 12 (2007), 171-181.
  • [17] Kumar, V. and Kumar, K., On the ideal convergence of sequences of fuzzy numbers, Inform. Sci. 178 (2008), 4670-4678.
  • [18] Matloka, M., Sequences of fuzzy numbers, Busefal, 28 (1986), 28-37.
  • [19] Mizumoto, M. and Tanaka, K., Some properties of fuzzy numbers, Advances in Fuzzy Set Theory and Applications, North-Holland (Amsterdam), 1979, 153-164.
  • [20] Mohiuddine, S.A., S. Şevli, H. and Cancan, M., Statistical convergence of double sequences in fuzzy normed spaces, Filomat, 26(4) (2012), 673-681.
  • [21] Mursaleen, M. and Edely, O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223-231.
  • [22] Nabiev, A., Pehlivan, S. and Gürdal, M., On I-Cauchy sequences, Taiwanese J. Math. 11(2) (2007) 569-5764.
  • [23] Nanda, S., On sequences of fuzzy numbers, Fuzzy Sets Syst. 33 (1989), 123-126.
  • [24] Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289-321.
  • [25] Rath, D. and Tripaty, B.C., On statistically convergence and statistically Cauchy sequences, Indian J. Pure Appl. Math. 25(4) (1994), 381-386.
  • [26] Saadati, R., On the I-fuzzy topological spaces, Chaos, Solitons and Fractals, 37 (2008), 1419-1426.
  • [27] Salat, T., Tripaty, B.C. and Ziman, M., On I-convergence eld, Ital. J. Pure Appl. Math. 17 (2005), 45-54.
  • [28] Savaş, E. and Mursaleen, M., On statistically convergent double sequences of fuzzy numbers, Inform. Sci. 162 (2004), 183{-92
  • [29] S. Şençimen, C. and Pehlivan, S., Statistical convergence in fuzzy normed linear spaces,Fuzzy Sets and Systems, 159 (2008), 361-370.
  • [30] Schoenberg, I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375.
  • [31] Tripathy, B. and Tripathy, B.C., On I-convergent double sequences, Soochow J. Math. 31 (2005), 549-560.
  • [32] Turkmen, M. R. and Dündar, E., On Lacunary Statistical Convergence of Double Sequences and Some Properties in Fuzzy Normed Spaces, Journal of Intelligent and Fuzzy Systems, DOI: 10.3233/JIFS-18841 (Pre-press).
  • [33] Zadeh, L.A., Fuzzy sets, Information and Control 8(1965), 338-353.

On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces

Year 2019, Volume: 7 Issue: 2, 405 - 409, 15.10.2019

Erdinç Dundar , Muhammed Recai Türkmen

Abstract

In this paper first, we investigate some properties of $\mathcal{I}_2$-convergence in fuzzy normed spaces. After, we study some relationships between $\mathcal{I}_2$-convergence  and $\mathcal{I}_2^{*}$-convergence of double sequences in fuzzy normed spaces.

Keywords

Double sequences $\mathcal{I}_2$-convergence $\mathcal{I}_2$-Cauchy Fuzzy normed space

References

  • [1] Bag, T. and Samanta, S.K., Fixed point theorems in Felbin's type fuzzy normed linear spaces, J. Fuzzy Math. 16(1) (2008), 243-260.
  • [2] Bede, B. and Gal, S.G., Almost periodic fuzzy-number-valued functions, Fuzzy Sets Syst. 147(2004), 385-403.
  • [3] Das, P., Kostyrko, P., Wilczynski, W. and Malik, P., I and I*-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620.
  • [4] Das, P. and Malik, P., On extremal I-limit points of double sequences, Tatra Mt. Math. Publ. 40 (2008), 91-102.
  • [5] Diamond, P. and Kloeden, P., Metric Spaces of Fuzzy Sets-Theory and Applications, World Scienti c Publishing, Singapore (1994).
  • [6] Dündar, E. and Altay, B., I2-convergence and I2-Cauchy of double sequences, Acta Mathematica Scientia, 34(2) (2014), 343-353.
  • [7] Dündar, E. and Altay, B., On some properties of I2-convergence and I2-Cauchy of double sequences, Gen. Math. Notes, 7(1) (2011), 1-12.
  • [8] Dündar, E. and Talo,  O., I2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems, 10(3) (2013), 37-50
  • [9] Dündar, E. and Talo,  O., I2-Cauchy Double Sequences of Fuzzy Numbers, Gen. Math. Notes, 16(2) (2013), 103-114.
  • [10] Fang, J.-X. and Huang, H., On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets Systems, 147 (2004), 417-415.
  • [11] Fast, H., Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [12] Felbin, C., Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48(2) (1992), 239-248.
  • [13] Hazarika, B., On ideal convergent sequences in fuzzy normed linear spaces, Afrika Matematika, 25(4) (2013), 987-999.
  • [14] Hazarika, B. and Kumar, V., Fuzzy real valued I-convergent double sequences in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, 26 (2014), 2323-2332.
  • [15] Kostyrko, P., Salat, T. and Wilczynski, W., I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • [16] Kumar, V., On I and I*-convergence of double sequences, Math. Commun. 12 (2007), 171-181.
  • [17] Kumar, V. and Kumar, K., On the ideal convergence of sequences of fuzzy numbers, Inform. Sci. 178 (2008), 4670-4678.
  • [18] Matloka, M., Sequences of fuzzy numbers, Busefal, 28 (1986), 28-37.
  • [19] Mizumoto, M. and Tanaka, K., Some properties of fuzzy numbers, Advances in Fuzzy Set Theory and Applications, North-Holland (Amsterdam), 1979, 153-164.
  • [20] Mohiuddine, S.A., S. Şevli, H. and Cancan, M., Statistical convergence of double sequences in fuzzy normed spaces, Filomat, 26(4) (2012), 673-681.
  • [21] Mursaleen, M. and Edely, O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223-231.
  • [22] Nabiev, A., Pehlivan, S. and Gürdal, M., On I-Cauchy sequences, Taiwanese J. Math. 11(2) (2007) 569-5764.
  • [23] Nanda, S., On sequences of fuzzy numbers, Fuzzy Sets Syst. 33 (1989), 123-126.
  • [24] Pringsheim, A., Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289-321.
  • [25] Rath, D. and Tripaty, B.C., On statistically convergence and statistically Cauchy sequences, Indian J. Pure Appl. Math. 25(4) (1994), 381-386.
  • [26] Saadati, R., On the I-fuzzy topological spaces, Chaos, Solitons and Fractals, 37 (2008), 1419-1426.
  • [27] Salat, T., Tripaty, B.C. and Ziman, M., On I-convergence eld, Ital. J. Pure Appl. Math. 17 (2005), 45-54.
  • [28] Savaş, E. and Mursaleen, M., On statistically convergent double sequences of fuzzy numbers, Inform. Sci. 162 (2004), 183{-92
  • [29] S. Şençimen, C. and Pehlivan, S., Statistical convergence in fuzzy normed linear spaces,Fuzzy Sets and Systems, 159 (2008), 361-370.
  • [30] Schoenberg, I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375.
  • [31] Tripathy, B. and Tripathy, B.C., On I-convergent double sequences, Soochow J. Math. 31 (2005), 549-560.
  • [32] Turkmen, M. R. and Dündar, E., On Lacunary Statistical Convergence of Double Sequences and Some Properties in Fuzzy Normed Spaces, Journal of Intelligent and Fuzzy Systems, DOI: 10.3233/JIFS-18841 (Pre-press).
  • [33] Zadeh, L.A., Fuzzy sets, Information and Control 8(1965), 338-353.
There are 33 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erdinç Dundar

Muhammed Recai Türkmen

Publication Date October 15, 2019
Submission Date April 14, 2019
Acceptance Date May 8, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Dundar, E., & Türkmen, M. R. (2019). On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces. Konuralp Journal of Mathematics, 7(2), 405-409.
AMA Dundar E, Türkmen MR. On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces. Konuralp J. Math. October 2019;7(2):405-409.
Chicago Dundar, Erdinç, and Muhammed Recai Türkmen. “On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 405-9.
EndNote Dundar E, Türkmen MR (October 1, 2019) On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces. Konuralp Journal of Mathematics 7 2 405–409.
IEEE E. Dundar and M. R. Türkmen, “On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces”, Konuralp J. Math., vol. 7, no. 2, pp. 405–409, 2019.
ISNAD Dundar, Erdinç - Türkmen, Muhammed Recai. “On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces”. Konuralp Journal of Mathematics 7/2 (October 2019), 405-409.
JAMA Dundar E, Türkmen MR. On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces. Konuralp J. Math. 2019;7:405–409.
MLA Dundar, Erdinç and Muhammed Recai Türkmen. “On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 405-9.
Vancouver Dundar E, Türkmen MR. On $\mathcal{I}_2$-Convergence and $\mathcal{I}_2^{*}$-Convergence of Double Sequences in Fuzzy Normed Spaces. Konuralp J. Math. 2019;7(2):405-9.
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