Ideal convergence and ideal equivalence of bounded linear functions in an n-normed linear space
Ideal converge
DOI:
https://doi.org/10.29304/jqcsm.2026.18.22763Keywords:
ideal Convergence, ideal Cauchy sequence, statistical convergence, statistical Cauchy ideal equivalent sequences.Abstract
An exploratory study of advanced convergence structures in linear n-norm spaces is presented in this paper with specific emphasis on examining bounded b-linear functionals. Building upon the classical theory of convergence, we develop both l-convergence and l-Cauchy sequences in linear n-normed spaces. An important result of our research is the concept of ideal equivalent sequences for bounded b-linear functionals which provides a strong theoretical framework for analyzing the equivalence of sequences of bounded b-linear functionals using ideals as a basis of comparison. Thus, using aspects of ideals, we characterize limiting behaviors in multidimensional normed structures more accurately.
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References
P.Kostyrko, T.Salat, W.Wilczynski, I-convergence, RealAnal.Exchange26(2)(2000)669–686
M.Katětov, Product soffilters, Comment.Math.Univ. Carolin 9(1968)173–189.
] S. Gahler, Lineare 2-normierte raume, Math. Nachr. 28, 1–43 (1964).
H.Steinhaus, Sur La Convergence Ordinaire et la Convergence Asymptotique, Colloq.Math 2(1951)73–74.
I.J.Schoenberg, The integrability of certain functions and related summability methods ,Amer .Math .Monthly 66(1959)361–375.
H.Halberstam, K.F.Roth, Sequences,I, Clarendon Press, Oxford,1966.
H. Gunawan, Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27, 631–639 (2001).
H.H.Ostmann,Additive ZahlentheorieI,Springer-Verlag,Berlin,1956.
A.Zygmund,Trigonometric Series,2nded.,CambridgeUniv.Press,Cambridge,1979.
J.Connor, The statistical and strong p-cesaro converge nceof sequences,Analysis8(1988)47–63.
R.Erdös,G.Tenenbaum, Surles densities decertainessuites d’entiers,Proc.Lond.Math. Soc 59(3)(1989)417–438.
A.R.Freedman, J.J.Sember, Densities and summability, Pacific J.Math.95(1981)293–305.
J.A.Fridy, On statistical convergence, Analysis5(1985)301–313.
H.I. Miller, A measure-theoretical subsequence characterizing national statistical convergence, Trans.Amer.Math.Soc.347(1995)1811–1819
S. Pehlivan, M.T.Karaev, Some results related to statistical convergence and Berezin symbols, J.Math.Anal.Appl.299(2)(2004)333–340.
S.Pehlivan,M.Gürdal,B.Fisher, Lacunary statistical cluster points of sequences, Math.Commun 11(2006)39–46.
G.DiMaio, Lj.D.R.Kočiniac, Statistical convergence in topology, Topology Appl 156(2008)28–45.
M.Balcerzak, K. Dems, A.Komisarski, Statistical convergence and ideal convergence for sequences of functions, J.Math.Anal. Appl 328(2007)715–729
S.Gähler,2-metris cheRäumeundIhre Topologis cheStruktur,Math.Nachr.26(1963)115–148.
A. L. Soenjaya, The Open Mapping Theorem in n-Banach space, International Journal of Pure and Applied Mathematics 74 (4), 593–597 (2012).
S.Gähler,A.H.Siddiqi,S.C.Gupta,Contribution stononar chimedean function alanalysis,Math.Nachr.69(1975)162–171.
H.Gunawan,Mashadi,Onfinitedimensional2-normedspaces,SoochowJ.Math.27(3)(2001)321–329
K. Dems, On I-Cauchy sequences, Real Anal. Exchange 3 (2004–2005) 123–128.
M.Gürdal,S.Pehlivan,Thestatisticalconvergencein2-Banachspaces,Thai.J.Math.2(1)(2004)107–113.
A.Şahiner, M.Gürdal, S.Saltan, H.Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11(4)(2007)1477–1484.
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