On uniform statistical convergence

References

[1] Ö. G. Atlihan, H. G. Ince and C. Orhan, Some variations of the Bohman–Korovkin theorem, Math. Comput. Modelling 50 (2009), no. 7–8, 1205–1210. 10.1016/j.mcm.2009.06.009Search in Google Scholar

[2] V. Baláž and T. Šalát, Uniform density u and corresponding I u -convergence, Math. Commun. 11 (2006), no. 1, 1–7. Search in Google Scholar

[3] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc. 576 (1996), 1–130. 10.1090/memo/0576Search in Google Scholar

[4] H. Bohman, On approximation of continuous and of analytic functions, Ark. Mat. 2 (1952), 43–56. 10.1007/BF02591381Search in Google Scholar

[5] J. Boos, Classical and Modern Methods in Summability, Oxford Math. Monogr., Oxford University, Oxford, 2000. 10.1093/oso/9780198501657.001.0001Search in Google Scholar

[6] T. C. Brown and A. R. Freedman, Arithmetic progressions in lacunary sets, Rocky Mountain J. Math. 17 (1987), no. 3, 587–596. 10.1216/RMJ-1987-17-3-587Search in Google Scholar

[7] T. C. Brown and A. R. Freedman, The uniform density of sets of integers and Fermat’s last theorem, C. R. Math. Rep. Acad. Sci. Canada 12 (1990), no. 1, 1–6. Search in Google Scholar

[8] J. Connor, K. Demirci and C. Orhan, Multipliers and factorizations for bounded statistically convergent sequences, Analysis (Munich) 22 (2002), no. 4, 321–333. 10.1524/anly.2002.22.4.321Search in Google Scholar

[9] G. Das, Sublinear functionals and a class of conservative matrices, Bull. Inst. Math. Acad. Sinica 15 (1987), no. 1, 89–106. Search in Google Scholar

[10] K. Demirci, A criterion for A-statistical convergence, Indian J. Pure Appl. Math. 29 (1998), no. 5, 559–564. Search in Google Scholar

[11] K. Demirci, ℐ -limit superior and limit inferior, Math. Commun. 6 (2001), no. 2, 165–172. Search in Google Scholar

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

[13] A. R. Freedman and J. J. Sember, Densities and summability, Pacific J. Math. 95 (1981), no. 2, 293–305. 10.2140/pjm.1981.95.293Search in Google Scholar

[14] J. A. Fridy, On statistical convergence, Analysis 5 (1985), no. 4, 301–313. 10.1524/anly.1985.5.4.301Search in Google Scholar

[15] J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3625–3631. 10.1090/S0002-9939-97-04000-8Search in Google Scholar

[16] K.-G. Grosse-Erdmann, The Blocking Technique, Weighted mean Operators and Hardy’s Inequality, Lecture Notes in Math. 1679, Springer, Berlin, 1998. 10.1007/BFb0093486Search in Google Scholar

[17] M. Gülfirat and N. Şahin Bayram, Multipliers and ℐ -core for sequences, Turkish J. Math. 45 (2021), no. 3, 1310–1318. 10.3906/mat-2102-97Search in Google Scholar

[18] K. Knopp, Zur Theorie der Limitierungsverfahren, Math. Z. 31 (1930), no. 1, 97–127. 10.1007/BF01246399Search in Google Scholar

[19] P. P. Korovkin, Linear Operators and Approximation Theory, Russian Monogr. Texts Adv. Math. Phys. 3, Gordon and Breach, New York, 1960. Search in Google Scholar

[20] P. Kostyrko, T. Šalát and W. Wilczyński, ℐ -convergence, Real Anal. Exchange 26 (2000/01), no. 2, 669–685. 10.2307/44154069Search in Google Scholar

[21] H. E. Lomelí and C. L. García, Variations on a theorem of Korovkin, Amer. Math. Monthly 113 (2006), no. 8, 744–750. 10.1080/00029890.2006.11920358Search in Google Scholar

[22] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190. 10.1007/BF02393648Search in Google Scholar

[23] I. J. Maddox, A new type of convergence, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 61–64. 10.1017/S0305004100054281Search in Google Scholar

[24] I. J. Maddox, On strong almost convergence, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 2, 345–350. 10.1017/S0305004100055766Search in Google Scholar

[25] I. J. Maddox, Some analogues of Knopp’s core theorem, Internat. J. Math. Math. Sci. 2 (1979), no. 4, 605–614. 10.1155/S0161171279000454Search in Google Scholar

[26] H. I. Miller and C. Orhan, On almost convergent and statistically convergent subsequences, Acta Math. Hungar. 93 (2001), no. 1–2, 135–151. Search in Google Scholar

[27] M. Mursaleen and O. H. H. Edely, Generalized statistical convergence, Inform. Sci. 162 (2004), no. 3–4, 287–294. 10.1016/j.ins.2003.09.011Search in Google Scholar

[28] C. Orhan, Sublinear functionals and Knopp’s core theorem, Internat. J. Math. Math. Sci. 13 (1990), no. 3, 461–468. 10.1155/S0161171290000680Search in Google Scholar

[29] C. Orhan and Ş. Yardimci, Banach and statistical cores of bounded sequences, Czechoslovak Math. J. 54(129) (2004), no. 1, 65–72. 10.1023/B:CMAJ.0000027247.75771.b3Search in Google Scholar

[30] S. Pehlivan, Strongly almost convergent sequences defined by a modulus and uniformly statistical convergence, Soochow J. Math. 20 (1994), no. 2, 205–211. Search in Google Scholar

[31] N. Şahin Bayram, Criteria for statistical convergence with respect to power series methods, Positivity 25 (2021), no. 3, 1097–1105. 10.1007/s11117-020-00801-6Search in Google Scholar

[32] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), no. 2, 139–150. Search in Google Scholar

[33] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. 10.2307/2308747Search in Google Scholar

[34] H. Steinhaus, Sur la convergence ordinaire et la convergence asymtotique, Colloq. Math. 2 (1951), no. 1, 73–74. Search in Google Scholar

[35] T. Yurdakadim and L. Miller-Van-Wieren, Some results on uniform statistical cluster points, Turkish J. Math. 41 (2017), no. 5, 1133–1139. 10.3906/mat-1607-21Search in Google Scholar