Deffered Rough $\mathcal{I}$-Statistical Convergence in $\mathcal{L}$-Fuzzy Normed Spaces
Resumen
The present article devoted to explore the concept of deffered rough statistical convergence of sequences through ideals in $\mathcal{L}$-fuzzy normed spaces. We introduce the notions of deffered rough ideal statistical limit points, deffered rough ideal cluster points, and deffered rough ideal boundedness within these spaces. Additionally, we examine the theory of convexity and closedness in relation to the set of approximate statistical limit points.
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[18] M. K¨u¸c¨ukaslan and M. Yilmazt¨urk. On deferred statistical convergence of sequences. Kyungpook Math. J., 56(2):357–366, 2016.
[19] B. K. Lahiri and P. Das. Further results on I-limit superior and limit inferior. Math. Commun., 8(2):151–156, 2003.
[20] P. Malik and M. Maity. On rough statistical convergence of double sequences in normed linear spaces. Afr. Mat., 27(1-2):141–148, 2016.
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[27] S. K. A. Rahaman and M. Mursaleen. On rough deferred statistical convergence of difference sequences in L-fuzzy normed spaces. J. Math. Anal. Appl., 530(2):127684, 2024.
[28] S. Shakeri, R. Saadati, and C. Park. Stability of the quadratic functional equation in non-archimedean L-fuzzy normed spaces. Int. J. Nonlinear Analysis Appl., 1(2):72–83, 2010.
[29] R. Yapali, H. C¸ o¸skun, and U. G¨urdal. Statistical convergence on L-fuzzy normed space. Filomat, 37(7):2077–2085, 2023.
[30] R. Yapali, E. Korkmaz, M. C¸ inar, and H. C¸ oskun. Lacunary statistical convergence on L-fuzzy normed space. J. Intell. Fuzzy Syst., 46(1):1985–1993, 2024.
[2] R. Antal, M. Chawla, and V. Kumar. Rough statistical convergence in probabilistic normed spaces. Thai J. Math., 20(4):1707–1719, 2023.
[3] R. Antal, M. Chawla, and V. Kumar. Certain aspects of rough ideal statistical convergence on neutrosophic normed spaces. Korean J. Math., 32(1):121–135, 2024.
[4] M. Arslan and E. D¨undar. On rough convergence in 2-normed spaces and some properties. Filomat, 33(16):5077–5086, 2019.
[5] S. Aytar. Rough statistical convergence. Numer. Funct. Anal. Optim., 29(3-4):291–303, 2008.
[6] M. Balcerzak, K. Dems, and A. Komisarski. Statistical convergence and ideal convergence for sequences of functions. J. Math. Anal. Appl., 328(1):715–729, 2007.
[7] A. K. Banerjee and A. Banerjee. A study on I-Cauchy sequences and I-divergence in s-metric spaces. Malaya J. Mat., 6(2, 2018):326–330, 2018.
[8] A. K. Banerjee and A. Paul. Rough I-convergence in cone metric spaces. J. Math. Comput. Sci., 12, 2022.
[9] G. Deschrijver, D. O’Regan, and S. M. Saadati, R.and Vaezpour. L-fuzzy euclidean normed spaces and compactness. Chaos Solitons Fractals, 42(1):40–45, 2009.
[10] M. Et, P. Baliarsingh, H.l Kandemir, and M. K¨u¸c¨ukaslan. On µ-deferred statistical convergence and strongly deferred summable functions. Rev. Real Acad. Cienc. Exactas Fis. Nat. - A: Mat., 115(1):34, 2021.
[11] Joseph A Goguen. L-fuzzy sets. J. Math. Anal. Appl., 18(1):145–174, 1967.
[12] H.Fast. Sur la convergence staistique. Colloq. Math., 2:241–244, 1951.
[13] A. H. Jan and T. Jalal. Pringsheim and lacunary δ-statistical convergence for double sequence on L-fuzzy normed space. Proyecciones, 43(6), 2024.
[14] V. A. Khan, M. Et, and I. A. Khan. Ideal convergence in modified IFNS and L-fuzzy normed space. Math. Found. Comput., pages 1–15, 2023.
[15] V. A. Khan, S. A. Rahaman, and B. Hazarika. On deferred I-statistical rough convergence of difference sequences in intuitionistic fuzzy normed spaces. Filomat, 38(18):6333–6354, 2024.
[16] P. Kostyrko, M. M´aˇcaj, T. Sal´at, and M. Sleziak. I-convergence and extremal I-limit points. Math. Slovaca, 55(4):443–464, 2005.
[17] P. Kostyrko, T. Sal´at, and W. Wilczy´nski. I-convergence. ˇ Real Anal. Exchange, 26(2):669–685, 2000.
[18] M. K¨u¸c¨ukaslan and M. Yilmazt¨urk. On deferred statistical convergence of sequences. Kyungpook Math. J., 56(2):357–366, 2016.
[19] B. K. Lahiri and P. Das. Further results on I-limit superior and limit inferior. Math. Commun., 8(2):151–156, 2003.
[20] P. Malik and M. Maity. On rough statistical convergence of double sequences in normed linear spaces. Afr. Mat., 27(1-2):141–148, 2016.
[21] M. Mursaleen, O. Ki¸si, and M. G¨urdal. On rough deferred statistical convergence for sequences in neutrosophic normed space. Filomat, 38(31):11171–11192, 2024.
[22] L. Nayak, B. C. Tripathy, and P. Baliarsingh. On deferred-statistical convergence of uncertain fuzzy sequences. Int. J. Gen. Syst., 51(6):631–647, 2022.
[23] A. Or, C¸ . Ahmet, A. Ozcan, and G. Karabacak. Rough statistical convergence in L-fuzzy normed spaces. International Journal of Advanced Natural Sciences and Engineering Researches, 7:307–314, 2023.
[24] S. K. Pal, C. H. Debraj, and S. Dutta. Rough ideal convergence. Hacet. J. Math. Stat., 42(6):633–640, 2013.
[25] H. X. Phu. Rough convergence in normed linear spaces. Numer. Funct. Anal. Optimiz., 22(1-2):199–222, 2001.
[26] H. X. Phu. Rough convergence in infinite dimensional normed spaces. Numer. Func. Anal. Optimiz., 24:285–301, 2003.
[27] S. K. A. Rahaman and M. Mursaleen. On rough deferred statistical convergence of difference sequences in L-fuzzy normed spaces. J. Math. Anal. Appl., 530(2):127684, 2024.
[28] S. Shakeri, R. Saadati, and C. Park. Stability of the quadratic functional equation in non-archimedean L-fuzzy normed spaces. Int. J. Nonlinear Analysis Appl., 1(2):72–83, 2010.
[29] R. Yapali, H. C¸ o¸skun, and U. G¨urdal. Statistical convergence on L-fuzzy normed space. Filomat, 37(7):2077–2085, 2023.
[30] R. Yapali, E. Korkmaz, M. C¸ inar, and H. C¸ oskun. Lacunary statistical convergence on L-fuzzy normed space. J. Intell. Fuzzy Syst., 46(1):1985–1993, 2024.
Publicado
2025-08-13
Sección
Advances in Nonlinear Analysis and Applications
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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