A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces

References

[1] B. Altay, F. J. García-Pacheco and R. Kama, On f-strongly Cesàro and f-statistical derivable functions, AIMS Math. 7 (2022), no. 6, 11276–11291. 10.3934/math.2022629Search in Google Scholar

[2] N. D. Aral and H. Şengül Kandemir, On f-lacunary statistical convergence of order β of double sequences for difference sequences of fractional order, Facta Univ. Ser. Math. Inform. 38 (2023), no. 2, 329–343. Search in Google Scholar

[3] V. K. Bhardwaj and S. Dhawan, Korovkin type approximation theorems via f-statistical convergence, J. Math. Anal. 9 (2018), no. 2, 99–117. 10.1186/s13660-018-1871-zSearch in Google Scholar PubMed PubMed Central

[4] M. Candan, Some characteristics of matrix operators on generalized Fibonacci weighted difference sequence space, Symmetry 14 (2022), no. 7, Article ID 1283. 10.3390/sym14071283Search in Google Scholar

[5] M. Candan and K. Kuddusi, Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, British J. Math. Comp. Sci. 7 (2015), no. 2, 150–167. 10.9734/BJMCS/2015/15923Search in Google Scholar

[6] R. Çolak and E. Kayan, df-statistical convergence of order α and df-strong Cesàro summability of order α in accordance to a modulus in metric spaces, Thai J. Math. 20 (2022), no. 2, 861–875. Search in Google Scholar

[7] S. Debnath and C. Choudhury, On I-statistically ϕ-convergence, Proyecciones 40 (2021), no. 3, 593–604. 10.22199/issn.0717-6279-4036Search in Google Scholar

[8] S. Debnath and B. C. Das, Some generalized triple sequence spaces defined by modulus function, Facta Univ. Ser. Math. Inform. 31 (2016), no. 2, 373–382. Search in Google Scholar

[9] S. Debnath, A. J. Datta and S. Saha, Regular matrix of interval numbers based on Fibonacci numbers, Afr. Mat. 26 (2015), no. 7–8, 1379–1385. 10.1007/s13370-014-0289-0Search in Google Scholar

[10] S. Debnath and S. Saha, Some newly defined Sequence spaces using regular matrix of Fibonacci numbers, AKU-J. Sci. Eng. 14 (2014), no. 1–3, Article ID 011301. 10.5578/fmbd.6907Search in Google Scholar

[11] S. Debnath and S. Saha, On some I-convergent generalized difference sequence spaces associated with multiplier sequence defined by a sequence of modulli, Proyecciones 34 (2015), no. 2, 137–146. 10.4067/S0716-09172015000200003Search in Google Scholar

[12] M. Et, M. Çınar and H. Şengül, On Δ m -asymptotically deferred statistical equivalent sequences of order α, Filomat 33 (2019), no. 7, 1999–2007. 10.2298/FIL1907999ESearch in Google Scholar

[13] M. Et, M. Cinar and H. Sengul Kandemir, Deferred statistical convergence of order α in metric spaces, AIMS Math. 5 (2020), no. 4, 3731–3740. 10.3934/math.2020241Search in Google Scholar

[14] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244. 10.4064/cm-2-3-4-241-244Search in Google Scholar

[15] J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), no. 1, 43–51. 10.2140/pjm.1993.160.43Search in Google Scholar

[16] S. G. Gal and I. T. Iancu, Korovkin-type theorems for statistically convergent sequences of monotone and sublinear operators, Bull. Malays. Math. Sci. Soc. 46 (2023), no. 2, Paper No. 79. 10.1007/s40840-023-01471-9Search in Google Scholar

[17] S. Gupta and V. K. Bhardwaj, On deferred f-statistical convergence, Kyungpook Math. J. 58 (2018), no. 1, 91–103. Search in Google Scholar

[18] I. S. Ibrahim and R. Çolak, On strong lacunary summability of order α with respect to modulus functions, An. Univ. Craiova Ser. Mat. Inform. 48 (2021), no. 1, 10.52846/ami.v48i1.1399. 10.52846/ami.v48i1.1399Search in Google Scholar

[19] I. S. Ibrahim and R. Çolak, λ-statistically convergent and λ-statistically bounded sequences defined by modulus functions, Bol. Soc. Parana. Mat. (3) 42 (2024), 10.5269/bspm.65818. 10.5269/bspm.65818Search in Google Scholar

[20] I. S. Ibrahim and M. C. Listán-García, The sets of ( α , β ) -statistically convergent and ( α , β ) -statistically bounded sequences of order γ defined by modulus functions, Rend. Circ. Mat. Palermo (2) (2024), 10.1007/s12215-024-00998-5. 10.1007/s12215-024-00998-5Search in Google Scholar

[21] M. Isik and K. E. Akbas, On asymptotically lacunary statistical equivalent sequences of order α in probability, ITM Web Conf. 13 (2017), Article ID 01024. 10.1051/itmconf/20171301024Search in Google Scholar

[22] M. Isik and K. E. Et, On lacunary statistical convergence of order α in probability, AIP Conf. Proc. 1676 (2015), Article ID 020045. 10.1063/1.4930471Search in Google Scholar

[23] R. Kama, Spaces of vector sequences defined by the f-statistical convergence and some characterizations of normed spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), no. 2, Paper No. 74. 10.1007/s13398-020-00806-6Search in Google Scholar

[24] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl. 2013 (2013), Paper No. 38. 10.1186/1029-242X-2013-38Search in Google Scholar

[25] E. E. Kara and M. Basarir, An application of Fibonacci numbers into infinite Toeplitz matrices, Casp. J. Math. Sci. 1 (2012), 43–47. Search in Google Scholar

[26] V. A. Khan, S. K. A. Rahaman and B. Hazarika, On statistical graph and pointwise convergence of sequences of set-valued functions defined on intuitionistic fuzzy normed spaces, Soft Comput. 27 (2023), no. 10, 1–16. 10.1007/s00500-023-07903-9Search in Google Scholar

[27] T. Koshy, Fibonacci and Lucas Numbers with Applications. Vol. 2, Pure Appl. Math. (Hoboken), John Wiley & Sons, Hoboken, 2019. 10.1002/9781118742297Search in Google Scholar

[28] F. León-Saavedra, M. C. Listán-García and M. P. Romero de la Rosa, On statistical convergence and strong Cesàro convergence by moduli for double sequences, J. Inequal. Appl. 2022 (2022), Paper No. 62. 10.1186/s13660-022-02799-9Search in Google Scholar

[29] M. C. Listán-García, f-statistical convergence, completeness and f-cluster points, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 2, 235–245. 10.36045/bbms/1464710116Search in Google Scholar

[30] M. C. Listán-García, On uniform f–statistical convergence of sequences of functions, Quaest. Math. 46 (2023), no. 8, 1643–1651. 10.2989/16073606.2022.2074909Search in Google Scholar

[31] I. J. Maddox, Inclusions between FK spaces and Kuttner’s theorem, Math. Proc. Cambridge Philos. Soc. 101 (1987), no. 3, 523–527. 10.1017/S0305004100066883Search in Google Scholar

[32] S. A. Mohiuddine and B. A. S. Alamri, Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 1955–1973. 10.1007/s13398-018-0591-zSearch in Google Scholar

[33] H. Nakano, Concave modulars, J. Math. Soc. Japan 5 (1953), 29–49. 10.2969/jmsj/00510029Search in Google Scholar

[34] M. P. Romero de la Rosa, On modulated lacunary statistical convergence of double sequences, Mathematics 11 (2023), no. 4, 1–10. 10.3390/math11041042Search in Google Scholar

[35] E. Savas and S. Debnath, Lacunary statistically ϕ-convergence, Note Mat. 39 (2019), no. 2, 111–119. 10.2298/PIM1919145SSearch in Google Scholar

[36] H. Şengül and M. Et, f-lacunary statistical convergence and strong f-lacunary summability of order α, Filomat 32 (2018), no. 13, 4513–4521. 10.2298/FIL1813513SSearch in Google Scholar

[37] H. Şengül, M. Et and Y. Altin, f-lacunary statistical convergence and strong f-lacunary summability of order α of double sequences, Facta Univ. Ser. Math. Inform. 35 (2020), no. 2, 495–506. 10.22190/FUMI2002495SSearch in Google Scholar

[38] H. Şengül, M. Et and M. Işık, On I-deferred statistical convergence of order α, Filomat 33 (2019), no. 9, 2833–2840. 10.2298/FIL1909833SSearch in Google Scholar

[39] H. Şengül, M. Işik and M. Et, On f-lacunary statistical convergence and strong f-lacunary summability of order ( α , β ) , J. Math. Anal. 10 (2019), no. 1, 40–48. Search in Google Scholar

[40] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math 2 (1951), 73–74. 10.4064/cm-2-2-98-108Search in Google Scholar

[41] F. Temizsu, M. Et, M. Çinar and H. Şengül Kandemir, On ( λ , f ) -statistical boundedness of order α, Comm. Statist. Theory Methods 51 (2022), no. 19, 6766–6776. 10.1080/03610926.2020.1866207Search in Google Scholar

[42] B. Torgut and Y. Altin, f-statistical convergence of double sequences of order α ~ , Proc. Nat. Acad. Sci. India Sect. A 90 (2020), no. 5, 803–808. 10.1007/s40010-019-00629-0Search in Google Scholar

[43] E. Yilmaz, T. Gulsen, Y. Altin and H. Koyunbakan, λ-Wijsman statistical convergence on time scales, Comm. Statist. Theory Methods 52 (2023), no. 15, 5364–5378. 10.1080/03610926.2021.2006716Search in Google Scholar

[44] M. Ç. Yilmazer, E. Yilmaz, S. Goktas and M. Et, Statistical convergence on non-Newtonian calculus, J. Anal. 31 (2023), no. 3, 2127–2137. 10.1007/s41478-023-00555-wSearch in Google Scholar