Some observations on generalized logarithmic statistical convergence of order $\rho$ for difference sequences via ideals
DOI:
https://doi.org/10.5269/bspm.77359Resumen
This paper explores various forms of logarithmic summability and statistical convergence for real sequences using generalized difference sequences and ideals. First, we introduce the concepts of logarithmic (Δ^{m},I)-statistical convergence of order Ï and logarithmic strong (Δ_{p}^{m},I)-Cesà ro summability of order Ï, analyzing their relationship. These notions are then extended to logarithmic Δ^{m}(f,I)-statistical convergence of order Ï and logarithmic strong Δ^{m}(f,I)-Cesà ro summability of order Ï, with fundamental connections established.
Referencias
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29. G¨urdal M., S¸ahiner A., A¸cık, I., Approximation theory in 2-Banach spaces, Nonlinear Anal., 71(5-6), 1654-1661, (2009).
2. Alghamdi, M. A., Mursaleen, M., Alotaibi, A., Logarithmic density and logarithmic statistical convergence, Adv. Differ. Equ., 227, 1-7, (2013).
3. Bhardwaj, V. K., Dhawan, S., f-statistical convergence of order α and strong Cesaro summability of order α with respect to a modulus, J. Inequal. Appl., 2015, 332:14, (2015).
4. Boztepe, A., D¨undar, E., Logarithmic ideal convergence, AK¨U FEM¨UBË™ID, 25, 89-94, (2025).
5. C¸ olak, R., Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub., 1, 121-129, (2010).
6. Das, P., Sava¸s, E., Ghosal, S. K., On generalizations of certain summability methods using ideals, Appl. Math. Lett., 24(9), 1509-1514, (2011).
7. Et, M., Strongly almost summable difference sequences of order m defined by a modulus, Stud. Sci. Math. Hung., 40(4), 463-476, (2003).
8. Et, M., Alotaibi, A., Mohiuddine, S. A., On (m, I)-statistical convergence of order α, Sci. World J., Article ID 535419, 5 pages, (2014).
9. Et, M., Altınok, H., Altın, Y., On generalized statistical convergence of order α of difference sequences, J. Funct. Spaces Appl., Article ID 370271, 7 pages, (2013).
10. Et, M., Ba¸sarır, M., On some new generalized difference sequence spaces, Period. Math. Hung., 35, 169-175, (1997).
11. Et, M., C¸ olak, R., On some generalized difference sequence spaces, Soochow J. Math., 21, 377-386, (1995).
12. Et, M., Gidemen, H., On mv (f)-statistical convergence of order α, Commun. Stat. Theory Methods, 49(14), 3521-3529, (2020).
13. Fast, H., Sur la convergence statistique, Colloq. Math., 2, 241-244, (1951).
14. Gadjiev, A. D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32(1), 129-138, (2002).
15. G¨urdal, M., S¸ahiner, A., Statistical approximation with a sequence of 2-Banach spaces, Math. Comput. Model., 55(3-4), 471-479, (2012).
16. G¨urdal, M., Sarı, N., Sava¸s, E., A-statistically localized sequences in n-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(2), 1484-1497, (2020).
17. G¨urdal, M., Yamanci, U., Statistical convergence and some questions of operator theory, Dynam. Systems Appl., 24 (7), 305-311, (2015).
18. Kadak, U., Mohiuddine, S. A., Generalized statistically almost convergence based on the difference operator which includes the p, q-gamma function and related approximation theorems, Results Math., 73, 9, (2018).
19. Kızmaz, H., On certain sequence spaces, Canad. Math. Bull., 24(2), 169-176, (1981).
20. Kostyrko, P., Salat, T., Wilczynski, W., I-convergence, Real Anal. Exchange, 26(2), 669-686, (2000/2001).
21. Maddox, I. J., Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc., 100, 161-166, (1986).
22. Mohiuddine, S. A., Statistical weighted A-summability with application to Korovkin’s type approximation theorem, J. Inequal. Appl., 2016, 101, (2016).
23. Mohiuddine, S. A., Alamri, B. A. S., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM, 113(3), 1955-1973, (2019).
24. Moricz, F., Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences, Analysis, 24, 127-145, (2004).
25. Nabiev, A., Sava¸s, E., G¨urdal, M., Statistically localized sequences in metric spaces, J. Appl. Anal. Comput., 9(2), 739-746, (2019).
26. Yamancı U., G¨urdal M., Statistical convergence and operators on Fock space, New York J. Math., 22, 199-207, (2016).
27. Yamancı U., G¨urdal M., On lacunary ideal convergence in random n-normed space, J. Math., 868457, 1-8, (2013).
28. Savas, E., Kisi, ¨ O., G¨urdal, M., On statistical convergence in credibility space, Numer. Funct. Anal. Optim., 43(8), 987-1008, (2022).
29. G¨urdal M., S¸ahiner A., A¸cık, I., Approximation theory in 2-Banach spaces, Nonlinear Anal., 71(5-6), 1654-1661, (2009).
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Publicado
2025-09-30
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Conf. Issue: Advances in Nonlinear Analysis and Applications
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Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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