$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces
Abstract
In this study, we introduced the concepts of $\mathcal{I}_2$-convergence and $\mathcal{I}_2^*$-convergence of double sequences of functions in $2$-normed space. Also, were studied some properties about these concepts and investigated relationships between them for double sequences of functions in $2$-normed spaces.
Keywords
References
- [1] M. Arslan, E. Dündar, I-Convergence and I-Cauchy Sequence of Functions In 2-Normed Spaces, Konuralp J. Math., 6(1) (2018), 57–62.
- [2] M. Arslan, E. Dündar, On I-Convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math., 42 (2018), 491–502.
- [3] M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl., 10(3) (2018), 1–9.
- [4] V. Balaz, J. Cervenansky, P. Kostyrko, T. Salat, I-convergence and I-continuity of real functions, Acta Math., Faculty of Natural Sciences, Constantine the Philosopher University, Nitra, 5 (2004), 43–50.
- [5] H. Çakalli, S. Ersan, New types of continuity in 2-normed spaces, Filomat, 30(3) (2016), 525–532.
- [6] P. Das, P. Kostyrko, W. Wilczy´nski, P. Malik, I and I-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605–620.
- [7] E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electron. J. Math. Anal. Appl., 3(1) (2015), 111–121.
- [8] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Math. Sci., 34B(2) (2014), 343–353.
- [9] E. Dündar, B. Altay, I2-uniform convergence of double sequences of functions Filomat, 30(5) (2016), 1273–1281.
- [10] E. Dündar, B. Altay, Multipliers for bounded I2-convergent of double sequences, Math. Comput. Modelling, 55(3-4) (2012), 1193–1198.
