References
- M. Arslan, E. Dundar, On I-convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math. 42 (2018), 491-502.
- N.L. Braha, H.M. Srivastava, S.A. Mohiuddine, A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallee Poussin mean, Appl. Math. Comput. 228 (2014), 162-169. https://doi.org/10.1016/j.amc.2013.11.095
- C. Belen, S.A. Mohiuddine, Generalized weighted statistical convergence and application, Appl. Math. Comput. 219 (2013), 9821-9826 https://doi.org/10.1016/j.amc.2013.03.115
- J.S. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull. 32 (1989), 194-198. https://doi.org/10.4153/CMB-1989-029-3
- C. Cakan, B. Altay, and M. Mursaleen, The σ-convergence and σ-core of double sequences, Appl. Math. Lett. 19 (2006), 1122-1128. https://doi.org/10.1016/j.aml.2005.12.003
- P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I*-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620. https://doi.org/10.2478/s12175-008-0096-x
- E. Dundar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Math. Sci. 34B(2) (2014), 343-353.
- E. Dundar, B. Altay, I2-uniform convergence of double sequences of functions, Filomat, 30(5) (2016), 1273-1281. https://doi.org/10.2298/FIL1605273D
- E. Dundar, N. Pancaroglu Akin, f-asymptotically Iσ-equivalence of real sequences, Konuralp J. Math. 8(1) (2020), 207-210
- E. Dundar, N. Pancaroglu Akin, f-asymptotically Iσθ-equivalence of real sequences, J. Math. Sci. Model. 3(1) (2020), 32-37.
- E. Dundar, N. Pancaroglu Akin, Wijsman lacunary ideal invariant convergence of double sequences of sets, Honam Math. J. 42(2) (2020), 345-358. https://doi.org/10.5831/HMJ.2020.42.2.345
- E. Dundar, U. Ulusu, F. Nuray, On asymptotically ideal invariant equivalence of double sequences, Thai J. Math. (in press).
- A. Esi, and M. Acikgoz, On λ2-asymptotically double statistical equivalent sequences, Int. J. Nonlinear Anal. Appl. 5 (2014), 16-21.
- A. Esi, On asymptotically double lacunary statistically equivalent sequences, Appl. Math. Lett. 22 (2009), 1781-1785. https://doi.org/10.1016/j.aml.2009.06.018
- B. Hazarika, V. Kumar, On Asymptotically double lacunary statistical equivalent sequences in ideal context, J. Inequal. Appl. 2013(543) (2013), DOI:10.1186/1029-242X2013-543
- B. Hazarika, On asymptotically ideal equivalent sequences, J. Egyptian Math. Soc. 23(1) (2015), 67-72. https://doi.org/10.1016/j.joems.2014.01.011
- B. Hazarika, A. Alotaibi, S.A. Mohiuddine, Statistical convergence inmeasure for double sequences of fuzzy-valued functions, Soft Comput. 24 (2020), 6613-6622 https://doi.org/10.1007/s00500-020-04805-y
- U. Kadak, S.A. Mohiuddine, Generalized statistically almost convergence based on the difference operator which includes the (p, q)-gamma function and related approximation theorems, Results Math. (2018) 73:9. https://doi.org/10.1007/s00025-018-0789-6
- E.E. Kara, M. Datan, M. Ilkhan, On lacunary ideal convergence of some sequences, New Trends Math. Sci. 5(1) (2017), 234-242.
- V.A. Khan, N. Khan, On some I-convergent double sequence spaces defined by a modulus function, Engineering, 5 (2013), 35-40. https://doi.org/10.4236/eng.2013.55A006
- G. Kilinc, I. Solak, Some double sequence spaces defined by a modulus function, Gen. Math. Notes, 25(2) (2014), 19-30.
- P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686. https://doi.org/10.2307/44154069
- V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Math. Sci. 6(23) (2012), 5 pages.
- V. Kumar, On I and I*-convergence of double sequences, Math. Commun. 12 (2007), 171-181.
- I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161-166. https://doi.org/10.1017/S0305004100065968
- M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-762. https://doi.org/10.1155/S0161171293000948
- S.A. Mohiuddine, 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 Fis. Nat., Ser. A Mat. RACSAM, 113(3) (2019), 1955-1973. https://doi.org/10.1007/s13398-018-0591-z
- S.A. Mohiuddine, A. Asiri, B. Hazarika, Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst. 48(5) (2019), 492-506. https://doi.org/10.1080/03081079.2019.1608985
- S.A. Mohiuddine, B. Hazarika, M.A. Alghamdi, Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560. https://doi.org/10.2298/fil1914549m
- M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9 (1983), 505-509.
- M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003) 223-231. https://doi.org/10.1016/j.jmaa.2003.08.004
- M. Mursaleen, S.A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62 (2012), 49-62. https://doi.org/10.2478/s12175-011-0071-9
- H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49. https://doi.org/10.2969/jmsj/00510029
- N. Pancaroglu Akin, f-asymptotically lacunary ideal equivalence of double sequences, J. Ineq. Appl. 2019 (2019), 1-11. https://doi.org/10.1186/s13660-019-1955-4
- F. Nuray, H. Gok, U. Ulusu, Iσ-convergence, Math. Commun. 16 (2011), 531-538.
- F. Nuray, E. Dundar, U. Ulusu, Wijsman I2-convergence of double sequences of closed sets, Pure Appl. Math. Lett. 2 (2014), 35-39.
- N. Pancaroglu, F. Nuray, Statistical lacunary invariant summability, Theoretical Math. Appl. 3(2) (2013), 71-78.
- N. Pancaroglu, F. Nuray, On invariant statistically convergence and lacunary invariant statistically convergence of sequences of sets, Progress Appl. Math. 5(2) (2013), 23-29.
- N. Pancaroglu, F. Nuray, Invariant statistical convergence of sequences of sets with respect to a modulus function, Abstr. Appl. Anal. 2014 (2014), 5 pages.
- N. Pancaroglu, F. Nuray, E. Savas, On asymptotically lacunary invariant statistical equivalent set sequences, AIP Conf. Proc. 1558(1) (2013), 780-781.
- N. Pancaroglu Akin, E. Dundar, U. Ulusu, Wijsman lacunary I-invariant convergence of sequences of sets, Proc. Nat. Acad. Sci. India Sect. A. (2020), DOI:10.1007/s40010-020-00694-w
- R.F. Patterson, Rates of convergence for double sequences, Southeast Asian Bull. Math. 26(3) (2002), 469-478. https://doi.org/10.1007/s10012-002-0469-y
- R.F. Patterson, E. Savas, Lacunary statistical convergence of double sequences, Math. Commun. 10 (2005), 55-61.
- R.F. Patterson, E. Savas, On asymptotically lacunary statistically equivalent sequences, Thai J. Math. 4(2) (2006), 267-272.
- S. Pehlivan, B. Fisher, Some sequences spaces defined by a modulus, Math. Slovaca, 45 (1995), 275-280.
- A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289-321. https://doi.org/10.1007/BF01448977
- R.A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81-94. https://doi.org/10.1215/S0012-7094-63-03009-6
- E. Savas, Strong σ-convergent sequences, Bull. Calcutta Math. 81 (1989), 295-300.
- E. Savas, F. Nuray, On σ-statistically convergence and lacunary σ-statistically convergence, Math. Slovaca, 43(3) (1993), 309-315.
- E. Savas, On I-asymptotically lacunary statistical equivalent sequences, Adv. Differ. Equ. 2013(111) (2013), DOI:10.1186/1687-1847-2013-111
- Y. Sever, U. Ulusu, E. Dundar, On strongly I and I*-lacunary convergence of sequences of sets, AIP Conf. Proc. 1611(1) (2014), 357-362.
- S. Tortop, E. Dundar, Wijsman I2-invariant convergence of double sequences of sets, J. Inequal. Spec. Funct. 9(4) (2018), 90-100.
- M.R. Turkmen, E. Dundar, On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces, J. Intell. Fuzzy Sys. 36(2) (2019), 1683-1690, DOI: 10.3233/JIFS-18841
- U. Ulusu, E. Dundar, Asymptotically I2-lacunary statistical equivalence of double sequences of sets, J. Ineq. Special Func. 7(2) (2016), 44-56.
- U. Ulusu, E. Dundar, B. Aydin, Asymptotically I2-Cesaro equivalence of double sequences of sets, J. Ineq. Special Func. 7(4) (2016), 225-234.
- U. Ulusu, E. Dundar, F. Nuray, Lacunary I2-invariant convergence and some properties, Int. J. Anal. Appl. 16(3) (2018), 317-327.
- U. Ulusu, E. Dundar, Asymptotically lacunary I2-invariant equivalence, J. Intell. Fuzzy Sys. 16(1) (2019), 467-472. https://doi.org/10.3233/JIFS-181796
- S. Yegul, E. Dundar, Statistical convergence of double sequences of functions and some properties in 2-normed spaces, Facta Univ. Ser. Math. Inform. 33(5) (2018), 705-719.