On Lacunary ideal convergence of some sequences

Yıl 2017, Cilt: 5 Sayı: 1, 234 - 242, 01.01.2017

Emrah Evren Kara , Mahmut Dastan Merve Ilkhan

Öz

In this paper, new classes of lacunary ideal
convergent and lacunary ideal bounded sequences combining an infinite matrix
and an Orlicz function are defined. Some properties of these spaces are
investigated and also some inclusion relations are obtained.

Anahtar Kelimeler

Invariant means, ideal convergence, Lacunary sequence

Kaynakça

• P. Das, Some further results on ideal convergence in topological spaces, Topology Appl. 159(10-11) (2012) 2621–2626.
• H. Fast, Sur la convergence statistique, Colloq. Math. 2(3-4) (1951) 241–244.
• A. R. Freedman, J. J. Sember and M. Raphael: Some Cesaro-type summability spaces, Proc. London Math. Soc. 37(3) (1978) 508–520.
• B. Hazarika, Strongly almost ideal convergent sequence spaces in a locally convex space defined by Musielak-Orlicz function, Iran. J. Math. Sci. Inform. 9(2) (2014) 15-35.
• M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1) (2006) 85–91.
• M. Gürdal and M. B. Huban, On I-convergence of double sequences in the Topology induced by random 2-norms, Mat. Vesnik 66(1) (2014) 73-83.
• M. Gürdal and A. Şahiner, Ideal Convergence in n-normed spaces and some new sequence spaces via n-norm, J. Fundamental Sci. 4(1) (2008) 233–244.
• E. E. Kara and M. İlkhan, On some paranormed A-ideal convergent sequence spaces defined by Orlicz function, Asian J. Math. Comput. Research 4(4) (2015) 183-194.
• E. E. Kara and M. İlkhan, Lacunary I-convergent and lacunary I-bounded sequence spaces defined by an Orlicz function, Electron. J. Math. Anal. Appl. 4(2) (2016) 150-159.
• A. Komisarski, Pointwise I-convergence and I- ^*convergence in measure of sequences of functions, J. Math. Anal. Appl. 340(2) (2008) 770-779.
• P. Kostyrko, W. Wilczynski and T. Salat, I-convergence, Real Anal. Exchange 26(2) (2000) 669–686.
• P. Kostyrko, M. Macaj, T. Salat and M. Sleziak, I-convergence and external I-limit points, Math. Slovaca 55(4) (2005) 443–464.
• P. K. Kamptan and M. Gupta, Sequence spaces and series, Marcel Dekker, New York, 1980.
• M. A. Krasnoselskii and Y. B. Rutitcky, Convex functions and Orlicz spaces, P.Noordhoff, Groningen, The Netherlands, 1961.
• B. K. Lahiri and P. Das, I and I*-convergence in topological spaces, Math. Bohem. 130(2) (2005) 153-160.
• J. Lindenstrauss and L. Tzafriri,On Orlicz sequence spaces, Israel J. Math. 10(3) (1971) 379-390.
• G. G. Lorentz, A contribution to the theory of divergent series, Act. Math. 80 (1948) 167-190.
• I. J. Maddox, Spaces of strongly summable sequences, Q. J. Math. 18 (1967) 345-355.
• S. A. Mohiuddine and M. Aiyub, Lacunary statistical convergence in random 2-normed spaces, Appl. Math. Inf. Sci. 6(3) (2012) 581-585.
• S. A. Mohiuddine and M. A. Alghamdi, Statistical summability through a lacunary sequence in locally solid Riesz spaces, J. Inequal. Appl. 2012 (2012) Article ID 225.
• M. Mursaleen and S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comput. Appl. Math. 233(2) (2009) 142–149.
• M. Mursaleen and A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca 61(6) (2011) 933-940.
• M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports 12(64)(4) (2010) 359-371.
• M. Mursaleen and S. A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca 62 (2012) 49-62.
• 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.
• P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972) 104-110.
• A. Şahiner,On I-lacunary strong convergence in 2-normed spaces, Int. J. Contempt. Math. Sciences 2(20) (2007) 991-998.
• A. Şahiner, M. Gürdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11(5) (2007) 1477–1484.
• B. C. Tripathy and B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca 59(4) (2009) 485–494.
• B. C. Tripathy and B. Hazarika, I-monotonic and I-convergent sequences, Kyungpook Math. J. 51 (2011) 233–239.
• B. C. Tripathy, B. Hazarika and B. Choudhary, Lacunary I-convergent sequences, Kyungpook Math. J. 52 (2012) 473–482.