On \(\mathcal{I}\)-Lacunary Double Statistical Convergence of Weight \(g\)

Ekrem Savas

Abstract


In this paper, our aim is to introduce new notions, namely, \(\mathcal{I}\)-statistical double convergence of weight \(g\) and \(\mathcal{I}\)-lacunary double statistical convergence of weight \(g\). We mainly investigate their relationship and also make some observations about these classes.

Keywords


Ideal; Filter; \(\mathcal{I}\)-double statistical convergence of weight \(g\); \(\mathcal{I}\)-lacunary double statistical convergence of weight \(g\); Closed subspace

Full Text:

PDF

References


M. Balcerzak, P. Das, M. Filipczak and J. Swaczyna, Generalized kinds of density and the associated ideals, Acta Math. Hungar. 147 (1) (2015), 97 – 115.

S. Bhunia, P. Das and S. Pal, Restricting statistical convergenge, Acta Math. Hungar. 134 (1-2) (2012), 153 – 161.

C. Cakan, B. Altay and H. Coskun, Double lacunary density and lacunary statistical convergence of double sequences, Studia Sci. Math. Hungar. 47 (1) (2010), 35 – 45.

R. Colak, Statistical convergence of order (alpha), Modern Methods in Analysis and its Applications, Anamaya Pub., New Delhi, India (2010), 121 – 129.

P. Das and S. Ghosal, Some further results on (I)-Cauchy sequences and condition (AP), Comp. Math. Appl. 59 (2010), 2597 – 2600.

P. Das, E. Sava¸s and S.K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters 24 (2011), 1509 – 1514.

P. Das and E. Savas, On (mathcal{I})-statistical and (mathcal{I})-lacunary statistical convergence of order (alpha), Bulletin of the Iranian Math. Soc. 40 (2) (2014), 459 – 472.

H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241 – 244.

J.A. Fridy, On statistical convergence, Analysis 5 (1985), 301 – 313.

J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), 43 – 51.

M. Gürdal and A. Sahiner, Ideal Convergence in-normed spaces and some new sequence spaces via-norm, Journal of Fundamental Sciences 4 (1) (2008), 233 – 244.

P. Kostyrko, T. Šalát and W. Wilczynki, (mathcal{I})-convergence, Real Anal. Exchange 26 (2) (2000/2001), 669 – 685.

B.K. Lahiri and P. Das, (mathcal{I}) and (mathcal{I}^*)-convergence in topological spaces, Math. Bohem. 130 (2005), 153 – 160.

B.K. Lahiri and P. Das, (mathcal{I}) and (mathcal{I}^*)-convergence of nets, Real Anal. Exchange 33 (2007-2008), 431 – 442.

M. Mursaleen and A. Alotaibi, Statistical summability and approximation by de la Vallée-Poussin mean, Appl. Math. Lett. 24 (2011), 320 – 324.

M. Mursaleen and S.A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, Jour. Comput. Appl. Math. 233 (2) (2009), 142 – 149.

M. Mursaleen and C. Belen, On statistical lacunary summability of double sequences, Filomat 28 (2) (2014), 231 – 239.

M. Mursaleen and O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (1) (2003), 223 – 231.

A. Nabiev, S. Pehlivan and M. Gürdal, On (mathcal{I})-Cauchy sequences, Taiwanese Journal of Mathematics 11 (2) (2003), 569 – 566.

T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139 – 150.

E. Savas, On lacunary strong (sigma)-convergence, Indian J. Pure Appl. Math. 21 (4) (1990), 359 – 365.

R.F. Patterson and E. Savas, Lacunary statistical convergence of double sequences, Math. Commun. 10 (2005), 55 – 61.

E. Savas and V. Karakaya, Some new sequence spaces defined by lacunary sequences, Math. Slovaca 57 (4) (2007), 393 – 399.

E. Sava¸s and P. Das, A generalized statistical convergence via ideals, Appl. Math. Letters 24 (2011), 826 – 830.

E. Savas, On generalized double statistical convergence via ideals, The Fifth Saudi Science Conference, 16-18 April, 2012.

E. Savas, P. Das and S. Dutta, A note on strong matrix summability via ideals, Appl. Math Letters 25 (4) (2012), 733 – 738.

E. Savas and R.F. Patterson, Lacunary statistical convergence of multiple sequences, Appl. Math. Lett. 19 (2006), 527 – 534.

E. Savas, On lacunary double statistical convergence in locally solid Riesz spaces, J. Inequal. Appl. 2013 (2013), 99.

E. Savas, Strong almost convergence and almost (lambda)-statistical convergence, Hokkaido Math. J. 29 (2000), 531 – 536.

E. Savas and M. Gürdal, Ideal convergent function sequences in random 2-normed spaces, Filomat 30 (3) (2016), 557 – 567.

I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361 – 375.


Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905