TY - JOUR T1 - On new modular sequence space defined over 2-normed spaces TT - 2-normlu uzaylarda tanımlı yeni modular dizi uzayı AU - Atıci Turan, Gülcan PY - 2020 DA - January DO - 10.25092/baunfbed.680685 JF - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi JO - BAUN Fen. Bil. Enst. Dergisi PB - Balıkesir University WT - DergiPark SN - 1301-7985 SP - 248 EP - 254 VL - 22 IS - 1 LA - en AB - In this paper, a new sequence space F(‖.,.‖,M,p,u) is defined by using a sequence of Orlicz functions in 2-normed spaces. Some various properties and some inclusions are also examined on this space. KW - Orlicz function KW - sequence spaces KW - 2-norm KW - paranormed spaces N2 - Bu çalışmada, 2-normlu uzaylarda Orlicz fonksiyonlarının bir dizisi kullanılarak F(‖.,.‖,M,p,u) yeni dizi uzayı tanımlanmıştır. Ayrıca bu uzayın bazı özellikleri ve bazı kapsama bağıntıları incelenmiştir. CR - Gähler, S., Uber 2-Banach räume, Mathematische Nachrichten, 42, 335-347, (1969). CR - Diminnie, C., Gähler, S. and White Jr. A.G., 2-inner product spaces, Demonstrario Mathematica, 6, 525-536, (1973). CR - White Jr. A.G., 2-Banach spaces, Mathematische Nachrichten, 42, 43-60, (1969). CR - Gähler, S., Siddiqi, A.H. and Gupta, S.C., Contributions to non-archimedean functional analysis, Mathematische Nachrichten, 69, 162-171, (1975). CR - Siddiqi, A.H., 2-normed spaces, The Aligarh Bulletin of Mathematics, 53-70, (1980). CR - Lindenstrauss, J., Tzafriri, L. On Orlicz sequence spaces, Israel Journal of Mathematics, 101, 379–390, (1971). CR - Gähler, S., Lineare 2-normierte Räume, Mathematische Nachrichten, 28, 1–43, (1965). CR - Maddox, I. J., Elements of functional analysis, Cambridge University Press, Cambridge, (1970). CR - Kamthan, P.K., Gupta, M., Sequence spaces and series, Marcel Dekker, New York, (1981). CR - Dutta, H., Kılıçman, A., Altun, Ö., Topological properties of some sequences defined over 2-normed spaces, SpringerPlus, 5, 2-16, (2016). CR - Dutta, H., Some statistically convergent difference sequence spaces defined over real 2-normed linear spaces, Applied Sciences, 12, 37–47, (2010). CR - Bektaş, Ç.A., Altin, Y., The sequence space l_M (p,q,s) on seminormed spaces, Indian Journal of Pure Applied Mathematics, 34(4), 529–534, (2003). CR - Rao, M.M., Ren, Z.D., Theory on Orlicz spaces, Marcel Dekker, New York, (1991). CR - Gürdal, M. and Şahiner, A., Ideal Convergence in n-normed spaces and some new sequence spaces via n-norm, Journal of Fundamental Sciences, 4(1), 233-244, (2008). CR - Şahiner, A., Gürdal, M., Saltan, S. and Gunawan, H., Ideal convergence in 2-normed spaces, Taiwanese Journal of Mathematics, 11(5), 1477-1484, (2007). CR - Şahiner, A. and Gürdal, M., New sequence spaces in n-normed spaces with respect to an Orlicz function, The Aligarh Bulletin of Mathematics, 27(1), 53-58, (2008). UR - https://doi.org/10.25092/baunfbed.680685 L1 - https://dergipark.org.tr/en/download/article-file/945974 ER -