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Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine

Year 2018, Volume: 18 Issue: 3, 868 - 877, 30.12.2018

Muhammed Recai Türkmen

Abstract

Bu çalışmada çift dizilerin lacunary ideal yakınsaklığı fuzzy n-norm kullanarak yeniden tanımlanmıştır. Çalışmada ilk olarak fuzzy n-normlu uzaylarda çift diziler için lacunary ideal yakınsaklık kavramına yer verilmiş, daha sonra bu yakınsama ile ilgili temel teoremlere değinilmiştir. İkinci olarak 𝜃-yakınsaklık kavramını fuzzy n-normlu uzaylarda çift diziler için tanıtıp, 𝜃-yakınsaklık ile lacunary ideal yakınsaklık arasındaki ilişki fuzzy n-normlu uzaylarda çift diziler için incelenmiştir. Son olarak, fuzzy n-normlu uzaylarda 𝐹𝑛𝜃2-Cauchy ve 𝐹𝑛ℐ2𝜃-Cauchy kavramları ve bu kavramlarla ilgili teoremlerin ifadeleri verilmiştir.

Keywords

Çift dizi İstatiksel yakınsaklık Lacunary yakınsaklık İdeal yakınsaklık Fuzzy n-norm.

References

  • Bag, T. and Samanta, S. K., 2008. Fixed point theorems in Felbin’s type fuzzy normed linear spaces. J. Fuzzy Math., 16(1), 243–260.
  • Debnath, P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers &Mathematics With Applications, 63(3), 708–715.
  • Diamond, P. and Kloeden, P., 1994. Metric Spaces of Fuzzy Sets-Theory and Applications. World Scientific Publishing, Singapore.
  • Dündar, E. and Talo, Ö., 2013a. ℐ2-convergence of double sequences of fuzzy numbers. Iranian Journal of Fuzzy Systems, 10(3), 37–50.
  • Dündar, E. and Talo, Ö., 2013b. ℐ2-Cauchy Double Sequences of Fuzzy Numbers. Gen. Math. Notes, 16(2), 103-114.
  • Dündar, E. and Altay, B., 2014. ℐ2-convergence and ℐ2-Cauchy of double sequences. Acta Mathematica Scientia, 34(2), 343–353.
  • Dündar, E., Ulusu, U. and Pancaroğlu, N., 2016. Strongly ℐ2-Lacunary Convergence and ℐ2-Lacunary Cauchy Double Sequences of Sets. The Aligarh Bulletin of Mathematics, 35(1,2), 1–15.
  • Fast, H., 1951. Sur la convergence statistique Colloq. Math., 2, 241–244.
  • Felbin, C., 1992. Finite-dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239–248.
  • Fridy, J. A., 1985. On statistical convergence. Analysis, 5, 301–313.
  • Fridy, J. A. and Orhan, C., 1993a. Lacunary statistical summability. Jour Math. Anal. Appl., 173(2), 497-504.
  • Fridy, J. A. and Orhan, C., 1993b. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43--51.
  • Hazarika, B., 2013. On ideal convergent sequences in fuzzy normed linear spaces. Afrika Matematika, 25(4), 987–999.
  • Hazarika, B. and Kumar, V., 2014. Fuzzy real valued ℐ-convergent double sequences in fuzzy normed spaces. Journal of Intelligent and Fuzzy Systems, 26, 2323–2332.
  • Hazarika, B., 2016. Lacunary ideal convergence of multiple sequences. Journal of the Egyptian Mathematical Society, 24, 54–59.
  • Kara, E. E. and İlkhan, M., 2016. Lacunary ℐ- convergent and lacunary ℐ -bounded sequence spaces defined by an Orlicz function. Electron. J. Math. Anal. Appl., 4(2), 150-159.
  • Kara, E. E., Dastan, M. and İlkhan, M., 2017. On Lacunary ideal convergence of some sequences. New Trends in Mathematical Sciences, 5(1), 234-242.
  • Katsaras, A. K., 1984. Fuzzy topological vector spaces. Fuzzy sets and systems, 12, 143—154.
  • Kostyrko, P., Šalát, T. and Wilczyński, W., 2000. ℐ-Convergence. Real Analysis Exchange, 26(2), 669—686.
  • Kostyrko, P., Macaj, M., Šalát, T. and Sleziak, M., 2005. ℐ-Convergence and Extermal ℐ-limits points. Mathematica Slovaca, 55, 443--464.
  • Kumar, V., 2007. On ℐ and ℐ∗-convergence of double sequences. Math. Commun., 12. 171–181.
  • Matloka, M., 1986. Sequences of fuzzy numbers. Busefal, 28. 28–37.
  • Mizumoto, M. and Tanaka, K., 1979. Some properties of fuzzy numbers Advances in Fuzzy Set Theory and Applications. North-Holland Amsterdam.
  • Mursaleen, M. and Edely, O. H. H., 2003. Statistical convergence of double sequences. J. Math. Anal. Appl., 28, 223–231.
  • Nanda, S., 1989. On sequences of fuzzy numbers. Fuzzy Sets Systems, 33, 123–126.
  • Narayan, A. L. and Vijayabalaji, S., 2005. Fuzzy n-normed linear space. International journal of mathematics and mathematical sciences, 24, 3963-3977
  • Nuray, F., 1989. Lacunary statistical convergence of sequences of fuzzy numbers. Fuzzy Sets and Systems, 99, 353–355.
  • Nuray, F. and Savaş, E., 1995. Statistical convergence of sequences of fuzzy numbers. Math. Slovaca, 45(3), 269–273.
  • Pringsheim, A., 1900. Zur theorie der zweifach unendlichen Zahlenfolgen. Math. Ann., 53, 289–321.
  • Rath, D. and Tripaty, B. C., 1994. On statistically convergence and statistically Cauchy sequences. Indian J. Pure Appl. Math., 25(4), 381–386.
  • Reddy, B. S., 2010. Statistical convergence in n-normed spaces. International Mathematical Forum, 5(24), 1185-1193.
  • Reddy, B. S. and Srinivas, M., 2015. Statistical Convergence in Fuzzy n-Normed Spaces. International Journal of Pure and Applied Mathematics, 104(1), 29-42.
  • Šalát, T., 1980. On statistically convergent sequences of real numbers. Math. Slovaca, 30, 139–150.
  • Šalát, T., Tripaty, B. C. and Ziman, M., 2005. On ℐ-convergence field. Ital. J. Pure Appl. Math., 17, 45–54.
  • Schoenberg, I. J., 1959. The integrability of certain functions and related summability methods. Amer. Math. Monthly, 66, 361–375.
  • Sencimen, C. and Pehlivan, S., 2008. Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems, 159, 361–370.
  • Tripathy, B. and Tripathy, B. C., 2005. On ℐ-convergent double sequences. Soochow J. Math., 31,549–560.
  • Tripathy, B. C., Hazarika, B. and Choudhary, B., 2012. Lacunary ℐ-convergent sequences. Kyungpook Math. J., 52, 473–482.
  • Türkmen, M. R., 2019a. On Lacunary ideal convergence and some properties in fuzzy normed spaces. under communication.
  • Türkmen, M. R. and Çınar, M., 2017. Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces. Applied and Computational Mathematics, 6(5), 233–237.
  • Türkmen, M. R. and Çınar, M., 2018. λ-Statistical Convergence in Fuzzy Normed Linear Spaces. Journal of Intelligent and Fuzzy Systems, 34(6), 4023–4030.
  • Türkmen, M. R. and Dündar, E., 2018. 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.
  • Türkmen, M. R., 2019b. On Lacunary İdeal Convergence and Some Properties in Fuzzy n-Normed Spaces. under communication.
  • Türkmen, M. R., 2018. On Lacunary Statistical Convergence and Some Properties in Fuzzy n-Normed Spaces. i-manager’s Journal on Mathematics.,7(3), preprint. Zadeh, L. A., 1965. Fuzzy sets. Inform. Contr., 8, 29-44.

Year 2018, Volume: 18 Issue: 3, 868 - 877, 30.12.2018

Muhammed Recai Türkmen

Abstract

References

  • Bag, T. and Samanta, S. K., 2008. Fixed point theorems in Felbin’s type fuzzy normed linear spaces. J. Fuzzy Math., 16(1), 243–260.
  • Debnath, P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers &Mathematics With Applications, 63(3), 708–715.
  • Diamond, P. and Kloeden, P., 1994. Metric Spaces of Fuzzy Sets-Theory and Applications. World Scientific Publishing, Singapore.
  • Dündar, E. and Talo, Ö., 2013a. ℐ2-convergence of double sequences of fuzzy numbers. Iranian Journal of Fuzzy Systems, 10(3), 37–50.
  • Dündar, E. and Talo, Ö., 2013b. ℐ2-Cauchy Double Sequences of Fuzzy Numbers. Gen. Math. Notes, 16(2), 103-114.
  • Dündar, E. and Altay, B., 2014. ℐ2-convergence and ℐ2-Cauchy of double sequences. Acta Mathematica Scientia, 34(2), 343–353.
  • Dündar, E., Ulusu, U. and Pancaroğlu, N., 2016. Strongly ℐ2-Lacunary Convergence and ℐ2-Lacunary Cauchy Double Sequences of Sets. The Aligarh Bulletin of Mathematics, 35(1,2), 1–15.
  • Fast, H., 1951. Sur la convergence statistique Colloq. Math., 2, 241–244.
  • Felbin, C., 1992. Finite-dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239–248.
  • Fridy, J. A., 1985. On statistical convergence. Analysis, 5, 301–313.
  • Fridy, J. A. and Orhan, C., 1993a. Lacunary statistical summability. Jour Math. Anal. Appl., 173(2), 497-504.
  • Fridy, J. A. and Orhan, C., 1993b. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43--51.
  • Hazarika, B., 2013. On ideal convergent sequences in fuzzy normed linear spaces. Afrika Matematika, 25(4), 987–999.
  • Hazarika, B. and Kumar, V., 2014. Fuzzy real valued ℐ-convergent double sequences in fuzzy normed spaces. Journal of Intelligent and Fuzzy Systems, 26, 2323–2332.
  • Hazarika, B., 2016. Lacunary ideal convergence of multiple sequences. Journal of the Egyptian Mathematical Society, 24, 54–59.
  • Kara, E. E. and İlkhan, M., 2016. Lacunary ℐ- convergent and lacunary ℐ -bounded sequence spaces defined by an Orlicz function. Electron. J. Math. Anal. Appl., 4(2), 150-159.
  • Kara, E. E., Dastan, M. and İlkhan, M., 2017. On Lacunary ideal convergence of some sequences. New Trends in Mathematical Sciences, 5(1), 234-242.
  • Katsaras, A. K., 1984. Fuzzy topological vector spaces. Fuzzy sets and systems, 12, 143—154.
  • Kostyrko, P., Šalát, T. and Wilczyński, W., 2000. ℐ-Convergence. Real Analysis Exchange, 26(2), 669—686.
  • Kostyrko, P., Macaj, M., Šalát, T. and Sleziak, M., 2005. ℐ-Convergence and Extermal ℐ-limits points. Mathematica Slovaca, 55, 443--464.
  • Kumar, V., 2007. On ℐ and ℐ∗-convergence of double sequences. Math. Commun., 12. 171–181.
  • Matloka, M., 1986. Sequences of fuzzy numbers. Busefal, 28. 28–37.
  • Mizumoto, M. and Tanaka, K., 1979. Some properties of fuzzy numbers Advances in Fuzzy Set Theory and Applications. North-Holland Amsterdam.
  • Mursaleen, M. and Edely, O. H. H., 2003. Statistical convergence of double sequences. J. Math. Anal. Appl., 28, 223–231.
  • Nanda, S., 1989. On sequences of fuzzy numbers. Fuzzy Sets Systems, 33, 123–126.
  • Narayan, A. L. and Vijayabalaji, S., 2005. Fuzzy n-normed linear space. International journal of mathematics and mathematical sciences, 24, 3963-3977
  • Nuray, F., 1989. Lacunary statistical convergence of sequences of fuzzy numbers. Fuzzy Sets and Systems, 99, 353–355.
  • Nuray, F. and Savaş, E., 1995. Statistical convergence of sequences of fuzzy numbers. Math. Slovaca, 45(3), 269–273.
  • Pringsheim, A., 1900. Zur theorie der zweifach unendlichen Zahlenfolgen. Math. Ann., 53, 289–321.
  • Rath, D. and Tripaty, B. C., 1994. On statistically convergence and statistically Cauchy sequences. Indian J. Pure Appl. Math., 25(4), 381–386.
  • Reddy, B. S., 2010. Statistical convergence in n-normed spaces. International Mathematical Forum, 5(24), 1185-1193.
  • Reddy, B. S. and Srinivas, M., 2015. Statistical Convergence in Fuzzy n-Normed Spaces. International Journal of Pure and Applied Mathematics, 104(1), 29-42.
  • Šalát, T., 1980. On statistically convergent sequences of real numbers. Math. Slovaca, 30, 139–150.
  • Šalát, T., Tripaty, B. C. and Ziman, M., 2005. On ℐ-convergence field. Ital. J. Pure Appl. Math., 17, 45–54.
  • Schoenberg, I. J., 1959. The integrability of certain functions and related summability methods. Amer. Math. Monthly, 66, 361–375.
  • Sencimen, C. and Pehlivan, S., 2008. Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems, 159, 361–370.
  • Tripathy, B. and Tripathy, B. C., 2005. On ℐ-convergent double sequences. Soochow J. Math., 31,549–560.
  • Tripathy, B. C., Hazarika, B. and Choudhary, B., 2012. Lacunary ℐ-convergent sequences. Kyungpook Math. J., 52, 473–482.
  • Türkmen, M. R., 2019a. On Lacunary ideal convergence and some properties in fuzzy normed spaces. under communication.
  • Türkmen, M. R. and Çınar, M., 2017. Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces. Applied and Computational Mathematics, 6(5), 233–237.
  • Türkmen, M. R. and Çınar, M., 2018. λ-Statistical Convergence in Fuzzy Normed Linear Spaces. Journal of Intelligent and Fuzzy Systems, 34(6), 4023–4030.
  • Türkmen, M. R. and Dündar, E., 2018. 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.
  • Türkmen, M. R., 2019b. On Lacunary İdeal Convergence and Some Properties in Fuzzy n-Normed Spaces. under communication.
  • Türkmen, M. R., 2018. On Lacunary Statistical Convergence and Some Properties in Fuzzy n-Normed Spaces. i-manager’s Journal on Mathematics.,7(3), preprint. Zadeh, L. A., 1965. Fuzzy sets. Inform. Contr., 8, 29-44.
There are 44 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Muhammed Recai Türkmen

Publication Date December 30, 2018
Submission Date September 24, 2018
Published in Issue Year 2018 Volume: 18 Issue: 3

Cite

APA Türkmen, M. R. (2018). Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 18(3), 868-877.
AMA Türkmen MR. Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2018;18(3):868-877.
Chicago Türkmen, Muhammed Recai. “Çift Dizilerin Fuzzy N-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı Ve Bazı Özellikleri Üzerine”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18, no. 3 (December 2018): 868-77.
EndNote Türkmen MR (December 1, 2018) Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18 3 868–877.
IEEE M. R. Türkmen, “Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 3, pp. 868–877, 2018.
ISNAD Türkmen, Muhammed Recai. “Çift Dizilerin Fuzzy N-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı Ve Bazı Özellikleri Üzerine”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18/3 (December 2018), 868-877.
JAMA Türkmen MR. Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18:868–877.
MLA Türkmen, Muhammed Recai. “Çift Dizilerin Fuzzy N-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı Ve Bazı Özellikleri Üzerine”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 3, 2018, pp. 868-77.
Vancouver Türkmen MR. Çift Dizilerin Fuzzy n-Normlu Uzaylarda Lacunary 𝓘𝟐-Yakınsaklığı ve Bazı Özellikleri Üzerine. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18(3):868-77.