Sage Journals: Discover world-class research

Abstract

In this paper, we introduce the notions of regularly $(I_{W_{2}}, I_{W})$ -convergence, regularly $(I_{W_{2}}^{*}, I_{W}^{*})$ -convergence, regularly $(I_{W_{2}}, I_{W})$ -Cauchy and regularly $(I_{W_{2}}^{*}, I_{W}^{*})$ -Cauchy double sequence of sets and investigate the relationship among them.

Keywords

Regularly ideal convergence,double sequence of sets,Wijsman convergence

Get full access to this article

View all access options for this article.

References

Altay

, Başar

, Some new spaces of double sequences, J Math Anal Appl 309(1) (2005), 70–90.

Aubin

J.-P.

, Frankowska

, Set-valued analysis, Birkhauser, Boston, (1990).

Baronti

, Papini

, Convergence of sequences of sets, In: Methods of functional analysis in aroximation theory, ISNM 76, Birkhauser-Verlag, Basel, (1986), pp. 133–155.

Beer

, On convergence of closed sets in a metric space and distance functions, Bull Aust Math Soc 31 (1985), 421–432.

Beer

, Wijsman convergence: A survey, Set-Valued Var Anal 2 (1994), 77–94.

Das

, Kostyrko

, Wilczyński

, Malik

I

and

I^{*}

-convergence of double sequences, Math Slovaca 58(5) (2008), 605–620.

Dündar

, Altay

I_{2}

-convergence and

I_{2}

-Cauchy of double sequences, Acta Mathematica Scientia 34B(2) (2014), 343–353.

Dündar

, Altay

, On some properties of

I_{2}

-convergence and

I_{2}

-Cauchy of double sequences, Gen Math Notes 7(1) (2011), 1–12.

Dündar

, Altay

I_{2}

-convergence of double sequences of functions, Electronic Journal of Mathematical Analysis and Applications 3(1) (2015), 111–121.

10.

Dündar

, Altay

I_{2}

-uniform convergence of double sequences of functions, Filomat 30(5) (2016), 1273–1281.

11.

Dündar

, Türkmen

M.R.

, Pancaroğlu Akın

, Regularly ideal convergence of double sequences in fuzzy normed spaces, (in review).

12.

Dündar

, Regularly (

I_{2}, I

)-Convergence and (

I_{2}, I

)-Cauchy Double Sequences of Functions, Pioneer Journal of Algebra, Number Theory and its Applications 1(2) (2011), 85–98.

13.

Dündar

, Ulusu

, Nuray

, On ideal invariant convergence of double sequences and some properties, Creative Mathematics and Informatics 27(2) (2018), 161–169.

14.

Dündar

, Ulusu

, Pancaroğlu

, , Strongly

I_{2}

-lacunary Convergence and

I_{2}

-lacunary Cauchy Double Sequences of Sets, The Aligarh Bulletin of Mathematics 35(1-2) (2016), 1–15.

15.

Fast

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

16.

Freedman

A.R.

, Sember

J.J.

, Raphael

, Some Cesàro type summability spaces, Proc London Math Soc 37 (1978), 508–520.

17.

Kişi

Ö.

and Nuray

, A new convergence for sequences of sets, Abstract and Applied Analysis 2013, Article ID 852796, 6 pages. http://dx.doi.org/10.1155/2013/852796.

18.

Kostyrko

, Šalát

and Wilczyński

I

-convergence, Real Anal Exchange 26(2) (2000), 669–686.

19.

Kumar

, On

I

and

I^{*}

-convergence of double sequences, Math Commun 12 (2007), 171–181.

20.

Mursaleen

O.H.

, Edely

, Statistical convergence of double sequences, J Math Anal Appl 288 (2003), 223–231.

21.

Nabiev

, Pehlivan

, Gürdal

, On

I

-Cauchy sequence, Taiwanese J Math 11(2) (2007), 569–576.

22.

Nuray

, Rhoades

B.E.

, Statistical convergence of sequences of sets, Fasc Math 49 (2012), 87–99.

23.

Nuray

, Ruckle

W.H.

, Generalized statistical convergence and convergence free spaces, J Math Anal Appl 245 (2000), 513–527.

24.

Nuray

, Dündar

, Ulusu

, Wijsman statistical convergence of double sequences of sets, Iranian Journal of Mathematical Sciences and Informatics, (In press).

25.

Nuray

, Dündar

, Ulusu

, Wijsman

I_{2}

-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters 2 (2014), 35–39.

26.

Nuray

, Ulusu

, Dündar

, Lacunary statistical convergence of double sequences of sets, Soft Computing 20(7) (2016), 2883–2888.

27.

Nuray

, Ulusu

, Dündar

, Esàro

, Summability of Double Sequences of Sets, General Mathematics Notes 25(1) (2014), 8–18.

28.

Pringsheim

, Zur theorie der zweifach unendlichen Zahlenfolgen, Math Ann 53 (1900), 289–321.

29.

Rockafellar

R.T.

, Wets

R.J.-B.

, Variational Analysis, Grundlehren der Mathematischen Wissenschaften 317, Springer-Verlag, 2009..

30.

Schoenberg

I.J.

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

31.

Sever

, Dündar

, Regularly Ideal Convergence and Regularly Ideal Cauchy Double Sequences in 2-Normed Spaces, Filomat 28(5) (2015), 907–915.

32.

Tripathy

, Tripathy

B.C.

, On

I

-convergent double sequences, Soochow J Math 31 (2005), 549–560.

33.

Türkmen

M.R.

, Dündar

, On Lacunary Statistical Convergence of Double Sequences and Some Properties in Fuzzy Normed Spaces, Journal of Intelligent and Fuzzy Systems 36(2) (2019), 1683–1690. doi:10.3233/JIFS-181796.

34.

Ulusu

, Dündar

, Asymptotically lacunary

I_{2}

-invariant equivalence, Journal of Intelligent and Fuzzy Systems 36(1) (2019), 467–472. doi:10.3233/JIFS-181796.

35.

Ulusu

, Dündar

I

-lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567–1574.

36.

Wijsman

R.A.

, Convergence of sequences of convex sets, cones and functions, Bull Amer Math Soc 70 (1964), 186–188.

37.

Wijsman

R.A.

, Convergence of Sequences of Convex sets, Cones and Functions II, Trans Amer Math Soc 123(1) (1966), 32–45.

Wijsman regularly ideal convergence of double sequences of sets

Abstract

Keywords

Get full access to this article

References