Research Article
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Year 2023, , 1 - 8, 28.03.2023
https://doi.org/10.54287/gujsa.1168439

Abstract

References

  • Ali, G., & Ansari, M. N. (2022). Multiattribute decision-making under Fermatean fuzzy bipolar soft framework. Granular Computing, 7(2), 337-352. doi:10.1007/s41066-021-00270-6
  • Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. doi:10.1016/S0165-0114(86)80034-3
  • Bilgin, N. G. (2022). Rough Statistical Convergence In Neutrosophic Normed Spaces. Euroasia Journal of Mathematics, Engineering, Natural & Medical Sciences, 9(21), 47-55. doi:10.38065/euroasiaorg.958
  • Bilgin, N. G., & Bozma, G. (2020). On Fuzzy n-Normed Spaces Lacunary Statistical Convergence of Order±. i-Manager's Journal on Mathematics, 9(2), 1-7. doi:10.26634/jmat.9.2.17841
  • Fast, H. (1951). Sur la convergence statistique. Colloquium Mathematicae, 2(3-4), 241-244.
  • Felbin, C. (1992). Finite-dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239-248. doi:10.1016/0165-0114(92)90338-5
  • Fradkov, A. L., & Evans, R. J. (2005). Control of chaos: methods and applications in engineering. Annual Reviews in Control, 29(1), 33-56. doi:10.1016/j.arcontrol.2005.01.001
  • Giles, R. (1980). A computer program for fuzzy reasoning. Fuzzy Sets and Systems, 4(3), 221-234. doi:10.1016/0165-0114(80)90012-3
  • Gonul Bilgin, N. (2022). Hibrid Δ-Statistical Convergence for Neutrosophic Normed Space. Journal of Mathematics, 2022, 3890308. doi:10.1155/2022/3890308
  • Gonul Bilgin, N., & Bozma, G. (2021). Fibonacci Lacunary Statistical Convergence of Order γ in IFNLS. International Journal of Advances in Applied Mathematics and Mechanics, 8(4), 28-36.
  • Guner, E., & Aygun, H. (2022). A New Approach to Fuzzy Partial Metric Spaces. Hacettepe Journal of Mathematics and Statistics, 51(6), 1-14. doi:10.15672/hujms.1115381
  • Khan, V. A., Khan, M. D., & Mobeen, A. (2019). Some results of neutrosophic normed spaces via fibonacci matrix, U.P.B Sci. Bull., Series A, 20(2), 1-14.
  • Khan, V. A., Alshlool, K. M. A. S., & Alam, M. (2020). On Hilbert I-convergent sequence spaces. Journal of Mathematics and Computer Science, 20(3), 225-233. doi:10.22436/jmcs.020.03.05
  • Khan, V. A., Ali., Abdullah, S. A. A., & Alshlool, K. M. A. S. (2022). On intuitionistic fuzzy hilbert ideal convergent sequence spaces. Acta Scientiarum. Technology, 44(1), e59724. doi:10.4025/actascitechnol.v44i1.59724
  • Kirisci, M. (2019). Fibonacci statistical convergence on intuitionistic fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems, 36(6), 5597-5604. doi:10.3233/jifs-181455
  • Kirisci M., & Simsek, N. (2020). Neutrosophic normed spaces and statistical convergence, Journal of Analysis, 28(4), 1059-1073. doi:10.1007/s41478-020-00234-0
  • Kisi, O. (2021a). Convergence Methods for Double Sequences and Applications in Neutrosophic Normed Spaces. In: Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences (pp. 137-154). CRC Press.
  • Kisi, O. (2021b). On Iθ-convergence in Neutrosophic Normed Spaces. Fundamental Journal of Mathematics and Applications, 4(2), 67-76. doi:10.33401/fujma.873029
  • Kisi, O. (2021c). Ideal convergence of sequences in neutrosophic normed spaces. Journal of Intelligent & Fuzzy Systems, 41(2), 2581-2590. doi:10.3233/JIFS-201568
  • Kisi O., & Guler E. (2019). On Fibonacci ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces. Turkish Journal of Mathematics and Computer Science, 11(Special Issue: Proceedings of ICMME 2019), 46-55.
  • Kostyrko, P., Salat, T., & Wilczynski, W. (2000). I-Convergence. Real Anal. Exchange, 26(2), 669-686.
  • Kumar, V., & Kumar, K. (2008). On the ideal convergence of sequences of fuzzy numbers. Information Sciences, 178(24), 4670-4678. doi:10.1016/j.ins.2008.08.013
  • Madore, J. (1992). Fuzzy physics Annals of Physics, 219(1), 187-198. doi:10.1016/0003-4916(92)90316-E
  • Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi, R. (2015). Intuitionistic fuzzy metric space. Notes on Intuitionistic Fuzzy Sets, 21(1), 43-53.
  • Mursaleen, M. (2000). Lambda-statistical convergence. Mathematica Slovaca, 50(1), 111–115.
  • Polat, H. (2016). Some new Hilbert sequence spaces. Muş Alparslan University Journal of Science, 4(1), 367-372.
  • Saadati, R., & Park, J. H. (2006). Intuitionistic fuzzy euclidean normed spaces. Communications in MathematicalAnalysis, 1(2), 85-90.
  • Savas, E., & Das, P. (2011). A generalized statistical convergence via ideals. Applied Mathematics Letters, 24(6), 826-830. doi:10.1016/j.aml.2010.12.022
  • Savas, E., & Gurdal, M. (2015). A generalized statistical convergence in intuitionistic fuzzy normed spaces. Science Asia, 41(4), 289-294. doi:10.2306/scienceasia1513-1874.2015.41.289
  • Smarandache, F., (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, Rehoboth, NM.
  • Smarandache, F. (2016). Degree of dependence and independence of the (sub)components of fuzzy set and neutrosophic set. Neutrosophic Sets and Systems, 11, 95-97. doi:10.5281/zenodo.50941
  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/S0019-9958(65)90241-X

Hilbert I-Statistical Convergence on Neutrosophic Normed Spaces

Year 2023, , 1 - 8, 28.03.2023
https://doi.org/10.54287/gujsa.1168439

Abstract

In this paper, λI-statistical convergence is defined to generalize statistical convergence on Neutrosophic normed spaces. As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects. Thus, researchers show great interest in this philosophical approach and try to transfer related topics to this field quickly. For this purpose, in this study, besides the definition of λI-statistical convergence, the important features of Hilbert sequence space and λI-statistical convergence in Neutrosophic spaces are examined with the help of these defined sequences. By giving the relationship between Hilbert λI-statistical convergence and Hilbert I-statistical convergence, it has been evaluated whether the definitions contain a coverage relationship as in fuzzy and intuitionistic fuzzy. As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types.

References

  • Ali, G., & Ansari, M. N. (2022). Multiattribute decision-making under Fermatean fuzzy bipolar soft framework. Granular Computing, 7(2), 337-352. doi:10.1007/s41066-021-00270-6
  • Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. doi:10.1016/S0165-0114(86)80034-3
  • Bilgin, N. G. (2022). Rough Statistical Convergence In Neutrosophic Normed Spaces. Euroasia Journal of Mathematics, Engineering, Natural & Medical Sciences, 9(21), 47-55. doi:10.38065/euroasiaorg.958
  • Bilgin, N. G., & Bozma, G. (2020). On Fuzzy n-Normed Spaces Lacunary Statistical Convergence of Order±. i-Manager's Journal on Mathematics, 9(2), 1-7. doi:10.26634/jmat.9.2.17841
  • Fast, H. (1951). Sur la convergence statistique. Colloquium Mathematicae, 2(3-4), 241-244.
  • Felbin, C. (1992). Finite-dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239-248. doi:10.1016/0165-0114(92)90338-5
  • Fradkov, A. L., & Evans, R. J. (2005). Control of chaos: methods and applications in engineering. Annual Reviews in Control, 29(1), 33-56. doi:10.1016/j.arcontrol.2005.01.001
  • Giles, R. (1980). A computer program for fuzzy reasoning. Fuzzy Sets and Systems, 4(3), 221-234. doi:10.1016/0165-0114(80)90012-3
  • Gonul Bilgin, N. (2022). Hibrid Δ-Statistical Convergence for Neutrosophic Normed Space. Journal of Mathematics, 2022, 3890308. doi:10.1155/2022/3890308
  • Gonul Bilgin, N., & Bozma, G. (2021). Fibonacci Lacunary Statistical Convergence of Order γ in IFNLS. International Journal of Advances in Applied Mathematics and Mechanics, 8(4), 28-36.
  • Guner, E., & Aygun, H. (2022). A New Approach to Fuzzy Partial Metric Spaces. Hacettepe Journal of Mathematics and Statistics, 51(6), 1-14. doi:10.15672/hujms.1115381
  • Khan, V. A., Khan, M. D., & Mobeen, A. (2019). Some results of neutrosophic normed spaces via fibonacci matrix, U.P.B Sci. Bull., Series A, 20(2), 1-14.
  • Khan, V. A., Alshlool, K. M. A. S., & Alam, M. (2020). On Hilbert I-convergent sequence spaces. Journal of Mathematics and Computer Science, 20(3), 225-233. doi:10.22436/jmcs.020.03.05
  • Khan, V. A., Ali., Abdullah, S. A. A., & Alshlool, K. M. A. S. (2022). On intuitionistic fuzzy hilbert ideal convergent sequence spaces. Acta Scientiarum. Technology, 44(1), e59724. doi:10.4025/actascitechnol.v44i1.59724
  • Kirisci, M. (2019). Fibonacci statistical convergence on intuitionistic fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems, 36(6), 5597-5604. doi:10.3233/jifs-181455
  • Kirisci M., & Simsek, N. (2020). Neutrosophic normed spaces and statistical convergence, Journal of Analysis, 28(4), 1059-1073. doi:10.1007/s41478-020-00234-0
  • Kisi, O. (2021a). Convergence Methods for Double Sequences and Applications in Neutrosophic Normed Spaces. In: Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences (pp. 137-154). CRC Press.
  • Kisi, O. (2021b). On Iθ-convergence in Neutrosophic Normed Spaces. Fundamental Journal of Mathematics and Applications, 4(2), 67-76. doi:10.33401/fujma.873029
  • Kisi, O. (2021c). Ideal convergence of sequences in neutrosophic normed spaces. Journal of Intelligent & Fuzzy Systems, 41(2), 2581-2590. doi:10.3233/JIFS-201568
  • Kisi O., & Guler E. (2019). On Fibonacci ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces. Turkish Journal of Mathematics and Computer Science, 11(Special Issue: Proceedings of ICMME 2019), 46-55.
  • Kostyrko, P., Salat, T., & Wilczynski, W. (2000). I-Convergence. Real Anal. Exchange, 26(2), 669-686.
  • Kumar, V., & Kumar, K. (2008). On the ideal convergence of sequences of fuzzy numbers. Information Sciences, 178(24), 4670-4678. doi:10.1016/j.ins.2008.08.013
  • Madore, J. (1992). Fuzzy physics Annals of Physics, 219(1), 187-198. doi:10.1016/0003-4916(92)90316-E
  • Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi, R. (2015). Intuitionistic fuzzy metric space. Notes on Intuitionistic Fuzzy Sets, 21(1), 43-53.
  • Mursaleen, M. (2000). Lambda-statistical convergence. Mathematica Slovaca, 50(1), 111–115.
  • Polat, H. (2016). Some new Hilbert sequence spaces. Muş Alparslan University Journal of Science, 4(1), 367-372.
  • Saadati, R., & Park, J. H. (2006). Intuitionistic fuzzy euclidean normed spaces. Communications in MathematicalAnalysis, 1(2), 85-90.
  • Savas, E., & Das, P. (2011). A generalized statistical convergence via ideals. Applied Mathematics Letters, 24(6), 826-830. doi:10.1016/j.aml.2010.12.022
  • Savas, E., & Gurdal, M. (2015). A generalized statistical convergence in intuitionistic fuzzy normed spaces. Science Asia, 41(4), 289-294. doi:10.2306/scienceasia1513-1874.2015.41.289
  • Smarandache, F., (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, Rehoboth, NM.
  • Smarandache, F. (2016). Degree of dependence and independence of the (sub)components of fuzzy set and neutrosophic set. Neutrosophic Sets and Systems, 11, 95-97. doi:10.5281/zenodo.50941
  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/S0019-9958(65)90241-X
There are 32 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Nazmiye Gönül Bilgin 0000-0001-6300-6889

Publication Date March 28, 2023
Submission Date August 30, 2022
Published in Issue Year 2023

Cite

APA Gönül Bilgin, N. (2023). Hilbert I-Statistical Convergence on Neutrosophic Normed Spaces. Gazi University Journal of Science Part A: Engineering and Innovation, 10(1), 1-8. https://doi.org/10.54287/gujsa.1168439