Deffered rough $\mathcal{i}$-statistical convergence in $\mathcal{l}$-fuzzy normed spaces
Abstract
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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References
Agnew, R. P., On deferred ces`aro means, Ann. Math. 33(3), 413–421, (1932).
Antal, R., Chawla, M. and Kumar, V., Rough statistical convergence in probabilistic normed spaces, Thai J. Math. 20(4), 1707–1719, (2022).
Antal, R., Chawla, M. and Kumar, V., Certain aspects of rough ideal statistical convergence on neutrosophic normed spaces, Korean J. Math. 32(1), 121–135, (2024).
Arslan, M. and D¨undar, E., On rough convergence in 2-normed spaces and some properties, Filomat, 33(16), 5077–5086, (2019).
Aytar, S., Rough statistical convergence, Numer. Funct. Anal. Optim. 29(3-4), 291–303, (2008).
Balcerzak, M., Dems, K. and Komisarski, A., Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328(1), 715–729, (2007).
Banerjee, A. K. and Banerjee, A., A study on I-Cauchy sequences and I-divergence in s-metric spaces, Malaya J. Mat. 6(2), 326–330, (2018).
Banerjee, A. K. and Paul, A., Rough I-convergence in cone metric spaces, J. Math. Comput. Sci. 12, Article ID 78, (2022).
Deschrijver, G., O’Regan, D., and Saadati, R.and Vaezpour, S. M., L-fuzzy euclidean normed spaces and compactness, Chaos Solitons Fractals, 42(1), 40–45, (2009).
Et, M., Baliarsingh, P., Kandemir, H. and K¨u¸c¨ukaslan, M., On μ-deferred statistical convergence and strongly deferred summable functions, Rev. Real Acad. Cienc. Exactas Fis. Nat. - A: Mat. 115, Article Number 7834, (2021).
Goguen, J. A., L-fuzzy sets, J. Math. Anal. Appl. 18(1), 145–174, (1967).
Fast, H., Sur la convergence staistique, Colloq. Math. 2, 241–244, (1951).
Jan, A. H. and Jalal, T., Pringsheim and lacunary δ-statistical convergence for double sequence on L-fuzzy normed space, Proyecciones, 43(6), 1347–1360, (2024).
Khan, V. A., Et, M. and Khan, I. A., Ideal convergence in modified IFNS and L-fuzzy normed space, Math. Found. Comput. pages 1–15, (2023).
Khan, V. A., Rahaman, S. A. and Hazarika, B., On deferred I-statistical rough convergence of difference sequences in intuitionistic fuzzy normed spaces, Filomat, 38(18), 6333–6354, (2024).
Kostyrko, P., M´aˇcaj, M., ˇSal´at, T. and Sleziak, M., I-convergence and extremal I-limit points, Math. Slovaca, 55(4), 443–464, (2005).
Kostyrko, P., ˇSal´at, T. and Wilczy´nski, W. (2000), I-convergence, Real Anal. Exchange, 26(2), 669–685, (2000).
K¨u¸c¨ukaslan, M. and Yilmazt¨urk, M., On deferred statistical convergence of sequences, Kyungpook Math. J. 56(2), 357–366, (2016).
Lahiri, B. K. and Das, P., Further results on I-limit superior and limit inferior, Math. Commun., 8(2), 151–156, (2003).
Malik, P. and Maity, M., On rough statistical convergence of double sequences in normed linear spaces, Afr. Mat. 27(1-2), 141–148, (2016).
Mursaleen, M., Ki¸si, ¨ O. and G¨urdal, M., On rough deferred statistical convergence for sequences in neutrosophic normed space, Filomat, 38(31), 11171–11192, (2024).
Nayak, L., Tripathy, B. C. and Baliarsingh, P., On deferred-statistical convergence of uncertain fuzzy sequences, Int. J. Gen. Syst. 51(6), 631–647, (2022).
Or, A., Ahmet, C¸ ., ¨ Ozcan, A. and Karabacak, G., Rough statistical convergence in L-fuzzy normed spaces, International Journal of Advanced Natural Sciences and Engineering Researches, 7, 307–314, (2023).
Pal, S. K., Debraj, C. H. and Dutta, S., Rough ideal convergence, Hacet. J. Math. Stat. 42(6), 633–640, (2013).
Phu, H. X. (2001), Rough convergence in normed linear spaces, Numer. Funct. Anal. Optimiz. 22(1-2), 199–222, (2001).
Phu, H. X., Rough convergence in infinite dimensional normed spaces, Numer. Func. Anal. Optimiz. 24, 285–301, (2003).
Rahaman, S. K. A. and Mursaleen, M., On rough deferred statistical convergence of difference sequences in L-fuzzy normed spaces, J. Math. Anal. Appl. 530(2), Article ID 127684, (2024).
Shakeri, S., Saadati, R. and Park, C., Stability of the quadratic functional equation in non-archimedean L-fuzzy normed spaces, Int. J. Nonlinear Analysis Appl. 1(2), 72–83, (2010).
Yapali, R., C¸ o¸skun, H. and G¨urdal, U., Statistical convergence on L-fuzzy normed space, Filomat, 37(7), 2077–2085, (2023).
Yapali, R., Korkmaz, E., C¸ inar, M. and C¸ oskun, H., Lacunary statistical convergence on L-fuzzy normed space, J. Intell. Fuzzy Syst. 46(1), 1985–1993, (2024).
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