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Bulanık Fark Dizilerinde Bir Modülüs Fonksiyonu Yardımıyla Tanımlı ρ-İstatistiksel Yakınsaklık Üzerine

Year 2024, Volume: 24 Issue: 2, 277 - 283, 29.04.2024

Damla Barlak

https://doi.org/10.35414/akufemubid.1364299

Abstract

Bu çalışmada ilk olarak bulanık sayı dizileri için ∆^m genelleştirilmiş fark operatörünü kullanarak ρ-istatistiksel yakınsaklık tanımını verdik. Ayrıca bulanık fark dizileri için kuvvetli N_F^ρ (∆^m,q)-toplanabilir dizi kümesini ve bir f modülüs fonksiyonu yardımıyla tanımlanan kuvvetli N_F^ρ (∆^m,f,q)-toplanabilir dizi kümesini tanımladık. Daha sonra bu kümelerle S_F^ρ (∆^m ) kümesi arasındaki bazı kapsama teoremlerini verdik.

Keywords

İststistiksel yakınsaklık Bulanık sayı dizisi Modülüs fonksiyonu Fark dizisi

References

  • Altınok, H. and Yağdıran, D., 2017. Lacunary statistical convergence defined by an Orlicz function in sequences of fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 32(3), 2725-2731. https:/doi.org/10.3233/JIFS-16842.
  • Aral, N.D., 2022. ρ-statistical convergence defined by modulus function of order (α,β). Maltepe Journal of Mathematics,4(1), 15-23. https:/doi.org/ 10.47087/mjm.1092599.
  • Aral, N.D., Kandemir, H.Ş. and Et. M., 2020. On ρ- Statistical convergence of sequences of Sets. Conference Proceeding Science and Tecnology, 3(1), 156-159. https:/doi.org/10.1063/5.0116105.
  • Aral, N.D., Kandemir, H. and Et, M., 2022. On ρ-statistical convergence of order α of sequences of function. e-Journal of Analysis and Applied Mathematics, 2022(1), 45-55.
  • Barlak, D., 2022. Statistically Convergence of Sequence of Fuzzy Numbers by a Modulus Function. ROMAI Journal, 18, 1-8.
  • Bektaş, Ç.A., Et, M. and Çolak, R., 2004 Generalized difference sequence spaces and their dual spaces. J. Math. Anal. Appl. 292, 423-432.
  • Çakallı, H., 2017. A variation on statistical ward continuity. Bull. Malays. Math. Sci. Soc. 40, 1701-1710. https:/doi.org /10.1007/s40840-015-0195-0.
  • Çakalli, H., Et, M. and Şengül, H., 2020. A variation on N_θ- ward continuity. Georgian Math. J. 27(2), 191—197. https:/doi.org/10.1515/gmj-2018-0037.
  • Et, M. and Çolak, R., 1995. On generalized difference sequence spaces. Soochow. J. Math. 21, 377-386.
  • Et, M. and Esi, A., 2000. On Köthe-Toeplitz duals of generalized difference sequence spaces. Bull. Malays. Math. Sci. Soc., 23, 25-32.
  • Fast, H., 1951. Sur la convergence statistique. Colloquium Math., 2, 241-244.
  • Gumus, H., 2022. Rho-statistical convergence of interval numbers. III. International Conference on Mathematics and Its Applications in Science and Engineering. Romania, 54.
  • Kandemir, H.Ş., 2022. On ρ-statistical convergence in topological groups. Maltepe Journal of Mathematics, 4(1), 9-14. https:/doi.org /10.47087/mjm. 1092559.
  • Karakaş, A., 2023. Some new generalized difference of sequences for fuzzy numbers. Soft Computing, 27(1), 47-55. https:/doi.org /10.1007/s00500-022-07601-y.
  • Karakaş, A., Altın, Y. and Altınok, H., 2014. On generalized statistical convergence of order β of sequences of fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 26(4), 1909-1917. https:/doi.org /10.3233/IFS-130869.
  • Kızmaz, H., 1981. On certain sequence spaces. Canad. Math. Bull. 24, 169-176.
  • Kwon, J.S., 2000. On statistical and p-Cesaro Convergence of fuzzy numbers. Korean J. Comput. & Appl. Math., 7(1), 195-203.
  • Matloka, M., 1986. Sequences of fuzzy numbers. BUSEFAL, 28, 28-37.
  • Nuray, F. and Savaş, E., 1995. Statistical convergence of sequences of fuzzy real numbers. Math. Slovaca 45(3), 269-273.
  • Schoenberg, I.J., 1959. The Integrability of Certain Functions and Related Summability Methods. Amer. Math. Monthly, 66, 361-375.
  • Steinhaus, H., 1951. Sur la convergence ordinaire et la convergence asymptotique Colloq. Math. 2, 73-74.
  • Şengül, H., Et, M. and Altin, Y., 2020. f-lacunary statistical convergence and strong f-lacunary summability of order α of double sequences. Facta Univ. Ser. Math. Inform. 35(2), 495—506.
  • Torgut, B. and Altin, Y., 2020.f-Statistical Convergence of Double Sequences of Order α. Proceedings of the National Academy of Sciences, India, Section A: Physical Sciences, 90, 803-808. https:/doi.org/10.1007/s40010-019-00629-0
  • Turan, G.A., 2017. On some topological properties of generalized difference sequence spaces defined. International Journal of Applied Mathematics, 3(2), 151-161. https:/doi.org /10.12732/ijam.v30i2.6.
  • Zadeh, L. A., 1965. Fuzzy sets. Inform and Control, 8, 338-353.

On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences

Year 2024, Volume: 24 Issue: 2, 277 - 283, 29.04.2024

Damla Barlak

https://doi.org/10.35414/akufemubid.1364299

Abstract

In this study, we first introduced the definition ∆_ρ^m-statistical convergence for sequences of fuzzy numbers using the generalized difference operator ∆^m. Furthermore, we defined the strong N_F^ρ (∆^m,q)-summable sequence set and the strong N_F^ρ (∆^m,f,q)-summable sequence set for fuzzy difference sequences aided by a modulus function f. Subsequently, we provided certain inclusion theorems between these sets and the S_F^ρ (∆^m ) set.

Keywords

Statistical convergence Sequence of fuzzy numbers Modulus function Difference sequence

References

  • Altınok, H. and Yağdıran, D., 2017. Lacunary statistical convergence defined by an Orlicz function in sequences of fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 32(3), 2725-2731. https:/doi.org/10.3233/JIFS-16842.
  • Aral, N.D., 2022. ρ-statistical convergence defined by modulus function of order (α,β). Maltepe Journal of Mathematics,4(1), 15-23. https:/doi.org/ 10.47087/mjm.1092599.
  • Aral, N.D., Kandemir, H.Ş. and Et. M., 2020. On ρ- Statistical convergence of sequences of Sets. Conference Proceeding Science and Tecnology, 3(1), 156-159. https:/doi.org/10.1063/5.0116105.
  • Aral, N.D., Kandemir, H. and Et, M., 2022. On ρ-statistical convergence of order α of sequences of function. e-Journal of Analysis and Applied Mathematics, 2022(1), 45-55.
  • Barlak, D., 2022. Statistically Convergence of Sequence of Fuzzy Numbers by a Modulus Function. ROMAI Journal, 18, 1-8.
  • Bektaş, Ç.A., Et, M. and Çolak, R., 2004 Generalized difference sequence spaces and their dual spaces. J. Math. Anal. Appl. 292, 423-432.
  • Çakallı, H., 2017. A variation on statistical ward continuity. Bull. Malays. Math. Sci. Soc. 40, 1701-1710. https:/doi.org /10.1007/s40840-015-0195-0.
  • Çakalli, H., Et, M. and Şengül, H., 2020. A variation on N_θ- ward continuity. Georgian Math. J. 27(2), 191—197. https:/doi.org/10.1515/gmj-2018-0037.
  • Et, M. and Çolak, R., 1995. On generalized difference sequence spaces. Soochow. J. Math. 21, 377-386.
  • Et, M. and Esi, A., 2000. On Köthe-Toeplitz duals of generalized difference sequence spaces. Bull. Malays. Math. Sci. Soc., 23, 25-32.
  • Fast, H., 1951. Sur la convergence statistique. Colloquium Math., 2, 241-244.
  • Gumus, H., 2022. Rho-statistical convergence of interval numbers. III. International Conference on Mathematics and Its Applications in Science and Engineering. Romania, 54.
  • Kandemir, H.Ş., 2022. On ρ-statistical convergence in topological groups. Maltepe Journal of Mathematics, 4(1), 9-14. https:/doi.org /10.47087/mjm. 1092559.
  • Karakaş, A., 2023. Some new generalized difference of sequences for fuzzy numbers. Soft Computing, 27(1), 47-55. https:/doi.org /10.1007/s00500-022-07601-y.
  • Karakaş, A., Altın, Y. and Altınok, H., 2014. On generalized statistical convergence of order β of sequences of fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 26(4), 1909-1917. https:/doi.org /10.3233/IFS-130869.
  • Kızmaz, H., 1981. On certain sequence spaces. Canad. Math. Bull. 24, 169-176.
  • Kwon, J.S., 2000. On statistical and p-Cesaro Convergence of fuzzy numbers. Korean J. Comput. & Appl. Math., 7(1), 195-203.
  • Matloka, M., 1986. Sequences of fuzzy numbers. BUSEFAL, 28, 28-37.
  • Nuray, F. and Savaş, E., 1995. Statistical convergence of sequences of fuzzy real numbers. Math. Slovaca 45(3), 269-273.
  • Schoenberg, I.J., 1959. The Integrability of Certain Functions and Related Summability Methods. Amer. Math. Monthly, 66, 361-375.
  • Steinhaus, H., 1951. Sur la convergence ordinaire et la convergence asymptotique Colloq. Math. 2, 73-74.
  • Şengül, H., Et, M. and Altin, Y., 2020. f-lacunary statistical convergence and strong f-lacunary summability of order α of double sequences. Facta Univ. Ser. Math. Inform. 35(2), 495—506.
  • Torgut, B. and Altin, Y., 2020.f-Statistical Convergence of Double Sequences of Order α. Proceedings of the National Academy of Sciences, India, Section A: Physical Sciences, 90, 803-808. https:/doi.org/10.1007/s40010-019-00629-0
  • Turan, G.A., 2017. On some topological properties of generalized difference sequence spaces defined. International Journal of Applied Mathematics, 3(2), 151-161. https:/doi.org /10.12732/ijam.v30i2.6.
  • Zadeh, L. A., 1965. Fuzzy sets. Inform and Control, 8, 338-353.
There are 25 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Damla Barlak 0000-0003-2992-1842

Early Pub Date April 14, 2024
Publication Date April 29, 2024
Submission Date September 21, 2023
Published in Issue Year 2024 Volume: 24 Issue: 2

Cite

APA Barlak, D. (2024). On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 24(2), 277-283. https://doi.org/10.35414/akufemubid.1364299
AMA Barlak D. On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2024;24(2):277-283. doi:10.35414/akufemubid.1364299
Chicago Barlak, Damla. “On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24, no. 2 (April 2024): 277-83. https://doi.org/10.35414/akufemubid.1364299.
EndNote Barlak D (April 1, 2024) On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24 2 277–283.
IEEE D. Barlak, “On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 24, no. 2, pp. 277–283, 2024, doi: 10.35414/akufemubid.1364299.
ISNAD Barlak, Damla. “On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24/2 (April 2024), 277-283. https://doi.org/10.35414/akufemubid.1364299.
JAMA Barlak D. On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2024;24:277–283.
MLA Barlak, Damla. “On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 24, no. 2, 2024, pp. 277-83, doi:10.35414/akufemubid.1364299.
Vancouver Barlak D. On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2024;24(2):277-83.
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