Almost and Strongly Almost B(r ̃,s ̃,t ̃,u ̃)- Summable Double Sequences
DOI:
https://doi.org/10.23918/eajse.v7i2p71Keywords:
Four-dimensional band matrix, matrix domain, almost convergence, double sequences, dual spaces, matrix transformationsAbstract
In this paper, we define some new almost and strongly almost convergent double sequence spaces B ̃(C_f), B ̃(C_f0), B ̃[C_f] and B ̃[C_f0] derived by the domain of four-dimensional sequential band matrix B(r ̃,s ̃,t ̃,u ̃) in the spaces C_f, C_f0 , [C_f] and [C_f0 ], respectively. Then we study some topological properties and prove some strict inclusion relations. Moreover, we calculate α-,β(bp)- and γ- duals of the new spaces. Finally, we state some known lemmas concerning the four-dimensional matrix classes of almost convergent double sequences, then we characterize some new four-dimensional matrix transformations from and into the new sequence spaces B ̃(C_f), and B ̃[C_f]. We conclude the paper with several significant results.
References
Adams, C. R. (1933). On non-factorable transformations of double sequences. Proc. Natl. Acad. Sci.
USA, 19(5), 564.
Basar, F., & Kirisci, M. (2011). Almost convergence and generalized difference matrix. Comput. Math.
Appl., 61(3), 602–611.
Basarir, M. (1995). On the strong almost convergence of double sequences. Period. Math. Hungar,
30(3), 177–181.
Capan, H., & Basar, F. (2019). On the difference spaces of almost convergent and strongly almost
convergent double sequences. Positivity, 23(2), 493–506.
Cunjalo, F. (2007). Almost convergence of double sequences-some analogies between measure and
category. Math. Maced, 5, 21–24.
Kayaduman, K., & Sengonul, M. (2012). The spaces of cesaro almost convergent sequences and core theorems. Acta Math. Sci. Ser. B, 32(6), 2265–2278.
Lorentz, G. G. (1948). A contribution to the theory of divergent sequences. Acta math., 80(1), 167–190.
Moricz, F., & Rhoades, B. (1988). Almost convergence of double sequences and strong regularity of
summability matrices. In Math. proc. cambridge philos. soc. (Vol. 104, pp. 283–294).
Moricz, F., & Rhoades, B. (1990). Some characterizations of almost convergence for single and double
sequences. In Proceedings of the 3rd annual meeting of the international workshop in analysis and its applications (Vol. 48, pp. 61–68).
Mursaleen. (2004). Almost strongly regular matrices and a core theorem for double sequences. J.
Math. Anal. Appl., 293(2), 523–531.
Mursaleen, & Savas¸, E. (2003). Almost regular matrices for double sequences. Studia Sci. Math.
Hungar., 40(1-2), 205–212.
Mursaleen, M. (2010). Almost convergence and some related methods. Modern Methods of Analysis
and Its Applications, 1–10.
Mursaleen, M., & Mohiuddine, S. (2009). Almost bounded variation of double sequences and some
four dimensional summability matrices. Publ. Math. Debrecen, 75(3-4), 495–508.
Mursaleen, M., & Mohiuddine, S. (2010). Invariant mean and some core theorems for double sequences.
Taiwanese J. Math., 14(1), 21–33.
Robison, G. M. (1926). Divergent double sequences and series. Trans. Amer. Math. Soc., 28(1), 50–73.
S¸engonul, M., & Kayaduman, K. (2012). On the Riesz almost convergent sequences space. In Abstr.
appl. anal. (Vol. 2012).
Tug, O. (2017a). Four-dimensional generalized difference matrix and almost convergent double sequence spaces. In Symposium functional analysis in interdisciplinary applications (pp. 83–87).
Tug, O. (2017b). Four-dimensional generalized difference matrix and some double sequence spaces.
J. Inequal. Appl., 2017(1), 1–22.
Tug, O. (2021). The spaces of B(r,s,t,u) strongly almost convergent double sequences and matrix transformations. Bull. Sci. Math., 169, 102989.
Tug, O., & Basar, F. (2016). On the spaces of Norlund almost null and Norlund almost convergent
sequences. Filomat, 30(3), 773–783.
Tug, O. (2017). On the matrix domain in the sequence space Lu. Eurasian Journal of Science and
Engineering, 3(1), 204–211.
Tug, O. (2018). On almost b-summable double sequence spaces. J. Inequal. Appl., 2018(1), 1–19.
Tug, O. (2018). On the characterization of some classes of four-dimensional matrices and almost summable double sequences. Journal of Mathematics, 2018.
Tug, O., & Basar, F. (2016). Four-dimensional generalized difference matrix and some double sequence
spaces. In Aip conference proceedings (Vol. 1759, p. 020075).
Tug, O., Rakocevic, V., & Malkowsky, E. (2020). On the domain of the four-dimensional sequential
band matrix in some double sequence spaces. Mathematics, 8(5), 789.
Yesilkayagil, M., & Basar, F. (2016). On the characterization of a class of four-dimensional matrices
and steinhaus type theorems. Kragujevac J. Math., 40(1), 35–45.
Zeltser, M., Mursaleen, M., & Mohiuddine, S. (2009). On almost conservative matrix methods for
double sequence spaces. Publ. Math. Debrecen, 75(3–4), 387–399.
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