Statistical convergence of double sequences on product time scales

References

[1] R. Agarwal, M. Bohner, D. O’Regan and A. Peterson, Dynamic equations on time scales: a survey, J. Comput. Appl. Math. 141 (2002), no. 1–2, 1–26. 10.1016/S0377-0427(01)00432-0Search in Google Scholar

[2] Y. Altin, H. Koyunbakan and E. Yilmaz, Uniform statistical convergence on time scales, J. Appl. Math. 2014 (2014), Article ID 471437. 10.1155/2014/471437Search in Google Scholar

[3] M. Bohner and G. S. Guseinov, Partial differentiation on time scales, Dynam. Systems Appl. 13 (2004), no. 3–4, 351–379. 10.1007/978-3-319-47620-9_6Search in Google Scholar

[4] M. Bohner and G. S. Guseinov, Double integral calculus of variations on time scales, Comput. Math. Appl. 54 (2007), no. 1, 45–57. 10.1016/j.camwa.2006.10.032Search in Google Scholar

[5] M. Bohner and H. Koyunbakan, Inverse problems for Sturm–Liouville difference equations, Filomat 30 (2016), no. 5, 1297–1304. 10.2298/FIL1605297BSearch in Google Scholar

[6] M. Bohner and A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications, Birkhäuser, Boston, 2001. 10.1007/978-1-4612-0201-1Search in Google Scholar

[7] D. Borwein, Linear functionals connected with strong Cesàro summability, J. London Math. Soc. 40 (1965), 628–634. 10.1112/jlms/s1-40.1.628Search in Google Scholar

[8] A. Cabada and D. R. Vivero, Expression of the Lebesque Δ-integral on time scales as a usual Lebesque integral; application to the calculus of Δ-antiderivates, Math. Comput. Model. 43 (2006), 194–207. 10.1016/j.mcm.2005.09.028Search in Google Scholar

[9] J. Connor, Two valued measures and summability, Analysis 10 (1990), no. 4, 373–385. 10.1524/anly.1990.10.4.373Search in Google Scholar

[10] J. S. Connor, The statistical and strong p-Cesàro convergence of sequences, Analysis 8 (1988), no. 1–2, 47–63. 10.1524/anly.1988.8.12.47Search in Google Scholar

[11] M. Et, S. A. Mohiuddine and A. Alotaibi, On λ-statistical convergence and strongly λ-summable functions of order α, J. Inequal. Appl. 2013 (2013), Article ID 469. 10.1186/1029-242X-2013-469Search 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] J. A. Fridy, On statistical convergence, Analysis 5 (1985), no. 4, 301–313. 10.1524/anly.1985.5.4.301Search in Google Scholar

[14] T. Gulsen and E. Yilmaz, Spectral theory of Dirac system on time scales, Appl. Anal. 96 (2017), no. 16, 2684–2694. 10.1080/00036811.2016.1236923Search in Google Scholar

[15] G. S. Guseinov, Integration on time scales, J. Math. Anal. Appl. 285 (2003), no. 1, 107–127. 10.1016/S0022-247X(03)00361-5Search in Google Scholar

[16] S. Hilger, Analysis on measure chains—a unified approach to continuous and discrete calculus, Results Math. 18 (1990), no. 1–2, 18–56. 10.1007/BF03323153Search in Google Scholar

[17] I. J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Cambridge Philos. Soc. 104 (1988), no. 1, 141–145. 10.1017/S0305004100065312Search in Google Scholar

[18] F. Móricz, Statistical convergence of multiple sequences, Arch. Math. (Basel) 81 (2003), no. 1, 82–89. 10.1007/s00013-003-0506-9Search in Google Scholar

[19] F. Móricz, Statistical limits of measurable functions, Analysis (Munich) 24 (2004), no. 1, 1–18. 10.1524/anly.2004.24.14.1Search in Google Scholar

[20] Mursaleen and O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), no. 1, 223–231. 10.1016/j.jmaa.2003.08.004Search in Google Scholar

[21] J. A. Osikiewicz, Summability of Matrix Submethods and Spliced Sequences, ProQuest LLC, Ann Arbor, 1997; PhD thesis – Kent State University. Search in Google Scholar

[22] A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), no. 3, 289–321. 10.1007/BF01448977Search in Google Scholar

[23] D. Rath and B. C. Tripathy, Matrix maps on sequence spaces associated with sets of integers, Indian J. Pure Appl. Math. 27 (1996), no. 2, 197–206. Search in Google Scholar

[24] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. 10.1080/00029890.1959.11989303Search in Google Scholar

[25] M. S. Seyyidog̃lu and N. O. Tan, On a generalization of statistical cluster and limit points, Adv. Difference Equ. 2015 (2015), Article ID 55. 10.1186/s13662-015-0395-9Search in Google Scholar

[26] M. S. Seyyidoglu and N. O. Tan, A note on statistical convergence on time scale, J. Inequal. Appl. 2012 (2012), 219–227. 10.1186/1029-242X-2012-219Search in Google Scholar

[27] 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

[28] B. C. Tripathy, Statistically convergent double sequences, Tamkang J. Math. 34 (2003), no. 3, 231–237. 10.5556/j.tkjm.34.2003.314Search in Google Scholar

[29] B. C. Tripathy and B. Sarma, Statistically convergent difference double sequence spaces, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 5, 737–742. 10.1007/s10114-007-6648-0Search in Google Scholar

[30] B. C. Tripathy and B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Math. Slovaca 59 (2009), no. 6, 767–776. 10.2478/s12175-009-0162-zSearch in Google Scholar

[31] B. C. Tripathy and M. Sen, Paranormed I-convergent double sequence spaces associated with multiplier sequences, Kyungpook Math. J. 54 (2014), no. 2, 321–332. 10.5666/KMJ.2014.54.2.321Search in Google Scholar

[32] C. Turan and O. Duman, Convergence methods on time scales, AIP Conf. Proc. 1558 (2013), 1120–1123. 10.1063/1.4825704Search in Google Scholar

[33] C. Turan and O. Duman, Statistical convergence on timescales and its characterizations, Advances in Applied Mathematics and Approximation Theory, Springer Proc. Math. Stat. 41, Springer, New York (2013), 57–71. 10.1007/978-1-4614-6393-1_3Search in Google Scholar

[34] C. Turan and O. Duman, Fundamental properties of statistical convergence and lacunary statistical convergence on time scales, Filomat 31 (2017), no. 14, 4455–4467. 10.2298/FIL1714455TSearch in Google Scholar

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

[36] E. Yilmaz, Y. Altin and H. Koyunbakan, λ-statistical convergence on time scales, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 23 (2016), no. 1, 69–78. 10.1080/03610926.2021.2006716Search in Google Scholar

[37] A. Zygmund, Trigonometric Series. Vol. I, II, Cambridge University, Cambridge, 1977. Search in Google Scholar