Vakeel A. KHAN, Ayhan ESİ, Yasmeen YASMEEN, Hira FATİMA

On some generalised I-convergent sequence spaces of double interval numbers

In this article we introduce and study some spaces of I-convergent sequences of double interval numbers with the help of a double sequence F = ( fi, j) of modulii and double bounded sequence p = (pi, j) of positive real numbers. We study some topological and algebraic properties, prove the decomposition theorem and study some inclusion relations on these spaces.

Keywords:

Double interval numbers, ideal filter, double I-convergent sequence spaces, solid and monotone space, Banach space,

PDF

___

E. Ayhan and B. Hazarika, Some I-convergent of duoble ∧-interval number sequences defined by Orlicz function, Global, J. of Mathmatical Analysis,1,No. 3,110-116 (2013).
E. Ayhan, -sequence spces of interval numbers, Appl.Math. Inf., 8, No. 3, 1099-1102 (2014).
R. C. Buck, Generalized asymptotic density, Amer., J. Math.,75 , 335-346 (1953).
K. P. Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematical Science, 18, No. 2, 219-233 (2002).
P. S. Dwyer, Linear computation, New York, Wiley, (1951).
H. Fast, Sur la convergence statistique, Colloq. Math.,2, 241-244 (1951).
J. A. Fridy, On statistical convergence, Analysis, 5, 301-313 (1985).
V. A. Khan, mohd. Shafiq and K. Ebadullah, On paranorm I-convergent sequence spaces of interval numbers, J. of Nonlinear analysis and Optimisation (Theory and Application), 5, No. 1, 103-114 (2014).
V. K. Khan, Ahyan Esi. and Mohd. Shafiq, On paranorm BVI-convergent sequence spaces defined by an Orlicz function, Global Journal of Mathematical Analysis, 2, No. 2, 28-43 (2014).
V. A. Khan and Mohd. Shafiq, On some generalized I-convergent sequence spaces of interval numbers, 10, No. 3,00-00 (2014).
V. A. Khan, Suthep Suantai and K. Ebadullah, On some I-convergent sequence spaces defined by a sequence of modulii, J. of Nonlinear analysis and Optimisation, 3, No. 2, 145-152 (2012).
E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, Acta Comment. Univ. Tartu., 960, 41-50 (1993).
E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of moduli, Acta Comment. Univ. Tartu., 970 65-72 (1994).
P. Kostyrko, M. Macaj and T. Salat, Statistical convergence and I- convergence, Real Analysis Exchange.
P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Analysis Exchange 26, No. 2, 669-686 (2000).
R. E. Moore, Automatic error analysis in digital computation, LSMD-48421, Lockheed Missiles and Space Company, (1959). R. E.Moore and C. T. Yang, Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif., (1959).
M. Mursaleen and K. Noman Abdullah, On the spaces of -convergent and bounded sequences, Thai Journal of Mathematics, 8, No. 2, 311-329 (2010).
M. Mursaleen and K. Sharma Sunil, Spaces of I-convergeent sequences, Article ID 134534, 6 pages http://dx.doi. org/10.1155/2014/134534 (2014).
H. Nakano, Concave modulars, J. Math Soc. Japan, 5, 29-49 (1953).
W. H. Ruckle, n perfect symmetric BK-spaces, Math. Ann., 175, 121-126 (1968).
W. H. Ruckle, Symmetric coordinate spaces and symmetric bases, Canad. J. Math., 19, 828-838 (1967).
W. H. Ruckle, FK-spaces in which the sequence of coordinate vector is bounded, Canad. J. Math., 25, No. 5, 973-975 (1973).
T. Salat, On statistical convergent sequences of real numbers, Math, Slovaca, 30(1980).
T. Salat, B. C. Tripathy and M. Ziman, On some properties of I-convergence, Tatra Mt. math. Publ., 28, 279-286 (2004).
T. Salat, B. C. Tripathy and M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math., 17, 45-54 (2005). [ I. J. Schoenberg,The integrability of certain functions and related summability methods, Amer.Math.Monthly, 66, 361-375 (1959). M. Sengonul and A. Eryilmaz, On the sequence spaces of interval numbers, Thai J. of Mathematics, 8, No. 3, 503-510 (2010).
B. C. Tripathy, On Statistical convergence, Proc. Estonian Acad. Sci. Phy. Math. Analysis, 299-303 (1998).
B. C. Tripathy and B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(2009), No. 4, 485-494 (2009).
B. K. Tripathy, B. C. Tripathy, On I-convergent double sequence, Soochow J. Math., 31(4) 549-560 (2005).
Yilmaz Yilmaz, Sumeyye Cakan and Sahika Aytekin, Topological quasilinear spaces, Hindawi Publishing Corporation, Abstract and Applied Analysis, (2012).