References
- W.H. Ruckle, Arithmetical summability, J. Math. Anal. Appl. 396 (2012), 741-748. https://doi.org/10.1016/j.jmaa.2012.06.048
- T. Yaying and B. Hazarika, On arithmetical summability and multiplier sequences, Natl. Acad. Sci. Lett. 40 (2017), 43-46. https://doi.org/10.1007/s40009-016-0525-2
- T. Yaying and B. Hazarika, On arithmetic continuity, Bol Soc Parana Mater. 35 (2017), 139-145. https://doi.org/10.5269/bspm.v35i1.27933
- T. Yaying, B. Hazarika and H. Cakalli, New results in quasi cone metric spaces, J Math Comput Sci. 16 (2016), 435-444. https://doi.org/10.22436/jmcs.016.03.13
- T. Yaying and B. Hazarika, On arithmetic continuity in metric spaces, Afr. Math. 28 (2017), 985-989. https://doi.org/10.1007/s13370-017-0498-4
- T. Yaying and B. Hazarika, Lacunary Arithmetic Statistical Convergence, Natl. Acad. Sci. Lett. 43 (2020), 547-551. https://doi.org/10.1007/s40009-020-00910-6
- H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
- J.A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301
- T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150.
- C. Belen and 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
- U. Kadak and 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. 73 (2018), 1-31. https://doi.org/10.1007/s00025-018-0773-1
- 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 Fis. Nat. Ser. A Math. 113 (2019), 1955-1973. https://doi.org/10.1007/s13398-018-0591-z
- S.A. Mohiuddine, A. Asiri and B. Hazarika, Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst. 48 (2019), 492-506. https://doi.org/10.1080/03081079.2019.1608985
- S.A. Mohiuddine, B. Hazarika and M.A. Alghamdi, Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat 33 (2019), 4549-4560. https://doi.org/10.2298/fil1914549m
- S.A. Mohiuddine, B. Hazarika and A. Alotaibi, On statistical convergence of double sequences of fuzzy valued functions, J. Intell. Fuzzy Syst. 32 (2017), 4331-4342. https://doi.org/10.3233/JIFS-16974
- B. Hazarika, A. Alotaibi and S.A. Mohiuddine, Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Computing 24 (2020), 6613-6622. https://doi.org/10.1007/s00500-020-04805-y
- A.R. Freedman, J.J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. Lond. Math. Soc. 37 (1978), 508-520.
- J. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8 (1988), 46-63. https://doi.org/10.1524/anly.1988.8.12.47
- R. Colak, Lacunary strong convergence of difference sequences with respect to a modulus function, Filomat 17 (2003), 9-14. https://doi.org/10.2298/FIL0317009C
- J.A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl. 173 (1993), 497-504. https://doi.org/10.1006/jmaa.1993.1082
- J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), 43-51. https://doi.org/10.2140/pjm.1993.160.43
-
P. Kostyrko, M. Macaj, T. Salat and M. Sleziak,
$\mathcal{I}$ -convergence and extremal$\mathcal{I}$ -limit points, Math. Slovaca 55 (2005), 443-464. - F. Nuray and W.H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513-527. https://doi.org/10.1006/jmaa.2000.6778
- P. Das, E. Savas and S.K. Ghosal, On generalized of certain summability methods using ideals, Appl. Math. Letter 36 (2011), 1509-1514.
-
E. Savas and M. Gurdal,
$\mathcal{I}$ -statistical convergence in probabilistic normed space, Sci. Bull. Series A Appl. Math. Physics 77 (2015), 195-204. -
M. Gurdal and M.B. Huban, On
$\mathcal{I}$ -convergence of double sequences in the Topology induced by random 2-norms, Mat. Vesnik 66 (2014), 73-83. -
M. Gurdal and A. Sahiner, Extremal
$\mathcal{I}$ -limit points of double sequences, Appl. Math. E-Notes 8 (2008), 131-137. - E. Savas and M. Gurdal, Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Syst. 27 (2014), 1621-1629. https://doi.org/10.3233/IFS-141128
- E. Savas and M. Gurdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia 41 (2015), 289-294. https://doi.org/10.2306/scienceasia1513-1874.2015.41.289
- E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), 826-830. https://doi.org/10.1016/j.aml.2010.12.022
- M. Mohiuddine and B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat 31 (2017), 1827-1834. https://doi.org/10.2298/FIL1706827M
- M. Mursaleen, S.A. Mohiuddine and O.H.H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl. 59 (2010), 603-611. https://doi.org/10.1016/j.camwa.2009.11.002
-
M. Mursaleen and A. Alotaibi, On
$\mathcal{I}$ -convergence in random 2-normed spaces, Math. Slovaca 61 (2011), 933-940. https://doi.org/10.2478/s12175-011-0059-5 - M. Mursaleen and 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
- M. Mursaleen and S.A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports 12 (2010), 359-371.
-
M. Mursaleen, S. Debnath and D. Rakshit,
$\mathcal{I}$ -statistical limit superior and$\mathcal{I}$ -statistical limit inferior, Filomat 31 (2017), 2103-2108. https://doi.org/10.2298/FIL1707103M -
E. Savas and H. Gumus, A generalization on
$\mathcal{I}$ -asymptotically lacunary statistical equivalent sequences, J Inequal Appl. 2013 (2013), 1-9. https://doi.org/10.1186/1029-242x-2013-1