ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

Ömer Kişi

DOI Number
https://doi.org/10.22190/FUMI201027032K
First page
435
Last page
448

Abstract


In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.

Keywords

ideal; $I2$-lacunary statistical convergence; intuitionistic fuzzy normed space; banach space; strongly convergence.

Full Text:

PDF

References


bibitem{atanassov} {sc K. T. Atanassov}: Itextit{ntuitionistic fuzzy sets}.

Fuzzy Sets and Systems, textbf{20} (1986), 87-96.

bibitem{atanassovv} {sc K. Atanassov, sc G. Pasi {rm and} R. Yager}: textit{%

Intuitionistic fuzzy interpretations of multi-person multicriteria decision

making.} Proceedings of 2002 First International IEEE Symposium Intelligent

Systems, textbf{1} (2002), 115-119.

bibitem{bakery} {sc A. A. Bakery}: textit{Operator ideal of Cesaro type sequence

spaces involving lacunary sequence}. Abstr. Appl. Anal. textbf{2014}

Article ID 419560, 6 pages.

bibitem{Moh1} {sc C. Belen {rm and} S. A. Mohiuddine}: textit{Generalized weighted

statistical convergence and application}. Appl. Math. Comput. textbf{219}

(2013), 9821-9826.

bibitem{belyil} {sc C. Belen {rm and} M. Yi ldi ri m:}: textit{On generalized

statistical convergence of double sequences via ideals}. Ann. Univ. Ferrara,

textbf{58(1)} (2012), 11-20.

bibitem{cakan} {sc C. c{C}akan {rm and} B. Altay}: textit{Statistically boundedness

and statistical core of double sequences}. J. Math. Anal. Appl. textbf{317}

(2006), 690-697.

bibitem{cakann} {sc C. c{C}akan, sc B. Altay {rm and} H. c{C}oc{s}kun}: textit{%

Double lacunary density and lacunary statistical convergence of double

sequences.} Studia Sci. Math. Hungar. textbf{47(1)} (2010), 35-45.

bibitem{das} {sc P. Das {rm and} Skr Ghosal}: textit{Some further results on} $%

mathcal{I}$-textit{Cauchy sequences and condition (AP)}. Comput. Math.

Appl. textbf{59} (2010), 2597-2600.

bibitem{dass} {sc P. Das, sc E. Savac{s} {rm and} Skr Ghosal}: textit{On

generalizations of certain summability methods using ideals}. Appl. Math.

Lett. textbf{24} (2011), 1509-1514.

bibitem{d1} {sc P. Debnath}: textit{A generalised statistical convergence in

intuitionistic fuzzy n-normed linear spaces}. Ann. Fuzzy Math. Inform.

textbf{12(4)} (2016) 559-572.

bibitem{d5} {sc P. Debnath}: textit{A new type of convergence in intuitionistic

fuzzy normed linear spaces.} J. New Theory, textbf{15} (2017), 19-25.

bibitem{d9} {sc P. Debnath}: textit{Lacunary ideal convergence in

intuitionistic fuzzy normed linear spaces}. Comput. Math. Appl. textbf{63}

(2012), 708-715.

bibitem{d11} {sc P. Debnath}: textit{Results on lacunary difference ideal

convergence in intuitionistic fuzzy normed linear spaces}. J. Intell. Fuzzy

Syst. textbf{28} (2015), 1299-1306.

bibitem{d10} {sc P. Debnath {rm and} M. Sen}: textit{Some completeness results in

terms of infinite series and quotient spaces in intuitionistic fuzzy

textit{n}-normed linear spaces}. J. Intell. Fuzzy Syst. textbf{26} (2014), 975-782.

bibitem{fast} {sc H. Fast}: textit{Sur la convergence statistique}. Colloq.

Math. textbf{2} (1951), 241-244.

bibitem{fridy} {sc J. A Fridy}: textit{On statistical convergence}. Analysis,

textbf{5} (1985), 301-313.

bibitem{fridyorhan} {sc J. A Fridy {rm and} C. Orhan}: textit{Lacunary statistical

convergence}. Pacific Journal of Mathematics, textbf{160(1)} (1993), 43-51.

bibitem{fridyorhann} {sc J. A Fridy {rm and} C. Orhan}: textit{Lacunary statistical

summability}. J. Math. Anal. Appl. textbf{173} (1993), 497-504.

bibitem{george} {sc V. George, sc S. Romaguera {rm and} P. Veeramani}: textit{A note on

intuitionistic fuzzy metric spaces}. Chaos Solitons Fractals, 28 (2006),

-905.

bibitem{Hardy} {sc G. H. Hardy}: textit{On the convergence of certain multiple

series}. Math. Proc. Cambridge Philos. Soc. 19 (1917), 86-95.

bibitem{haz} {sc B. Hazarika}: textit{Lacunary ideal convergence of multiple

sequences}. J. Egyptian Math. Soc. textbf{24(1)} (2016), 54-59.

bibitem{Moh7} {sc B. Hazarika, sc A. Alotaibi {rm and} S. A. Mohiuddine}: textit{%

Statistical convergence in measure for double sequences of fuzzy-valued

functions.} Soft Computing, textbf{24} (2020), 6613-6622.

bibitem{hosseini} {sc S. B. Hosseini, sc D. O. Regan {rm and} R. Saadati}: textit{Some

results of intuitionistic fuzzy spaces}. Iran. J. Fuzzy Syst. textbf{4(1)}

(2007), 53-64.

bibitem{Moh2} {sc U. Kadak {rm and} S. A. Mohiuddine}: textit{Generalized

statistically almost convergence based on the difference operator which

includes the (p,q)-Gamma function and related approximation theorems}.

Results Math. textbf{73(9)} (2018), 1-31.

bibitem{karakus} {sc S. Karakuc{s}, sc K. Demirci {rm and} O. Duman}: textit{%

Statistical convergence on intuitionistic fuzzy normed spaces}. Chaos

Solitons Fractals, textbf{35} (2008), 763-769.

bibitem{kisi} {sc "{O}. Kic{s}i}: $mathcal{I}$-textit{lacunary statistical

convergence in intuitionistic fuzzy normed spaces}: Aku J. Sci. Eng. textbf{%

} (2020), 207-212.

bibitem{d8} {sc N. Konwar, sc B. Davvaz {rm and} P. Debnath}: textit{Results on

generalized intuitionistic fuzzy hypergroupoids}, J. Intell. Fuzzy Syst.

textbf{36(3)} (2019), 2571-2580.

bibitem{d7} {sc N. Konwar, sc B. Davvaz {rm and} P. Debnath}: textit{Approximation of

new bounded operators in intuitionistic fuzzy n-Banach spaces}. J. Intell.

Fuzzy Syst. textbf{35(6)} (2018), 6301-6312.

bibitem{d2} {sc N. Konwar {rm and} P. Debnath}: $I_{lambda }$-textit{convergence in

intuitionistic fuzzy n-normed linear space}. Ann. Fuzzy Math. Inform. textbf{13(1)} (2017), 91-107.

bibitem{d3} {sc N. Konwar {rm and} P. Debnath}: textit{Continuity and Banach

contraction principle in intuitionistic fuzzy n-normed linear spaces}. J.

Intell. Fuzzy Syst. textbf{33(4)} (2017), 2363-2373.

bibitem{d6} {sc N. Konwar {rm and} P. Debnath}: textit{Some new contractive

conditions and related fixed point theorems in intuitionistic fuzzy textit{n}-Banach

spaces}. J. Intell. Fuzzy Syst. textbf{34(1)} (2018), 361-372.

bibitem{kostyrko} {sc P. Kostyrko, sc T. Salat {rm and} W. Wilczynki}: $mathcal{I}$-%

textit{convergence}. Real Analysis Exchange, textbf{26(2)} (2000), 669-686.

bibitem{KumBhatia} {sc S. Kumar, sc V. Kumar {rm and} S. S. Bhatia}: On ideal version of

lacunary statistical convergence of double sequences, Gen. Math. Notes,

(1) (2013), 32-44.

bibitem{Lael} {sc F. Lael {rm and} K. Nourouzi}: textit{Some results on the

IF-normed spaces}. Chaos Solitons Fractals, textbf{37} (2008), 931-939.

bibitem{li} {sc J. Li}: textit{Lacunary statistical convergence and inclusion

properties between lacunary methods}. Int. J. Math. Math. Sci. textbf{23(3)}

(2000), 175-180.

bibitem{Moh3} {sc S. A. Mohiuddine {rm and} B. A. S. Alamri}: textit{Generalization of

equi-statistical convergence via weighted lacunary sequence with associated

Korovkin and Voronovskaya type approximation theorems}, Rev. R. Acad. Cienc.

Exactas F'{i}s. Nat. Ser. A Math. textbf{113(3)} (2019), 1955-1973.

bibitem{Moh4} {sc S. A. Mohiuddine, sc A. Asiri {rm and} B. Hazarika}: textit{Weighted

statistical convergence through difference operator of sequences of fuzzy

numbers with application to fuzzy approximation theorems}. Int. J. Gen.

Syst. textbf{48(5)} (2019), 492-506.

bibitem{Moh5} {sc S. A. Mohiuddine, sc B. Hazarika {rm and} M.A. Alghamdi}: textit{Ideal

relatively uniform convergence with Korovkin and Voronovskaya types

approximation theorems}. Filomat, textbf{33(14)} (2019), 4549-4560.

bibitem{Moh6} {sc S. A. Mohiuddine, sc B. Hazarika {rm and} A. Alotaibi}: textit{On

statistical convergence of double sequences of fuzzy valued functions}. J.

Intell. Fuzzy Syst. textbf{32} (2017), 4331-4342.

bibitem{mor} {sc F. Moricz}: textit{Tauberian theorems for Ces`{a}ro summable

double sequences}. Studia Math. textbf{110} (1994), 83-96.

bibitem{mur2} {sc M. Mursaleen {rm and} A. Alotaibi}: textit{On }$mathcal{I}$-%

textit{convergence in random 2-normed spaces}. Math. Slovaca, textbf{61(6)}

(2011), 933-940.

bibitem{mur5} {sc M. Mursaleen, sc S. Debnath {rm and} D. Rakshit}: $mathcal{I}$-%

textit{statistical limit superior and} $mathcal{I}$-textit{statistical

limit inferior}. Filomat, textbf{31(7)} (2017), 2103-2108.

bibitem{mursaleenedely} {sc M. Mursaleen {rm and} O.H.H. Edely}: textit{Statistical

convergence of double sequences}. J. Math. Anal. Appl. textbf{288} (2003),

-231.

bibitem{mur3} {sc M. Mursaleen {rm and} S. A. Mohiuddine}: textit{On ideal

convergence in probabilistic normed spaces}. Math. Slovaca, textbf{62(1)}

(2012), 49-62

bibitem{mur4} {sc M. Mursaleen {rm and} S. A. Mohiuddine}: textit{ On ideal

convergence of double sequences in probabilistic normed spaces}. Math.

Reports, textbf{12(62)4} (2010), 359-371.

bibitem{mursaleen} {sc M. Mursaleen {rm and} S. A. Mohiuddine}: textit{ On lacunary

statistical convergence with respect to the intuitionistic fuzzy normed space%

}. J. Comput. Appl. Math. textbf{233(2)} (2009), 142-149.

bibitem{mur1} {sc M. Mursaleen, sc S. A. Mohiuddine {rm and} O. H. H. Edely}: textit{On

the ideal convergence of double sequences in intuitionistic fuzzy normed

spaces}. Comput. Math. Appl. textbf{59} (2010), 603-611.

bibitem{park} {sc J. H. Park}: textit{Intuitionistic fuzzy metric spaces}.

Chaos Solitons Fractals, textbf{22} (2004), 1039-1046.

bibitem{pringsheim} {sc A. Pringsheim}: textit{Zur theorie der zweifach

unendlichen Zahlenfolgen}. Math. Ann. textbf{53} (1900), 289-321.

bibitem{salat} {sc T. Salat}: textit{On statistically convergent sequences of

real numbers}. Math. Slovaca, textbf{30} (1980), 139-150.

bibitem{savasdas} {sc E. Savac{s} {rm and} P. Das}: textit{A generalized

statistical convergence via ideals}. Appl. Math. Lett. textbf{24} (2011),

-30.

bibitem{savasgurdal} {sc E. Savac{s} {rm and} M. G"{u}rdal}: textit{A generalized

statistical convergence in intuitionistic fuzzy normed spaces}. Science

Asia, textbf{41} (2015), 289-294.

bibitem{d4} {sc M. Sen {rm and} P. Debnath}: textit{Statistical convergence in

intuitionistic fuzzy n-normed linear spaces}. Fuzzy Information and

Engineering, 3 (2011), 259-273.

bibitem{yurdal} {sc Y. Sever}: $alpha beta $-textit{statistical} $e$-textit{%

convergence for double sequences}. Aku J. Sci. Eng. textbf{20} (2020),

-46.

bibitem{tripathy} {sc B. C. Tripathy, sc B. Hazarika {rm and} B. Choudhary}: textit{%

Lacunary} $mathcal{I}$-textit{convergent sequences}, Kyungpook Math. J.

textbf{52(4)} (2012), 473-482.

bibitem{zadeh} {sc L. A. Zadeh}: textit{Fuzzy sets}. Inform. Control, textbf{8}

(1965), 338-353.




DOI: https://doi.org/10.22190/FUMI201027032K

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)