$\mathcal{I}_2$-Uniform Convergence of Double Sequences of Functions In $2$-Normed Spaces

In this work, we discuss various kinds of $\mathcal{I}_2$-uniform convergence and equi-continuous for double sequences of functions and introduce the concepts of $\mathcal{I}_2$-uniform convergence, $\mathcal{I}_2^*$-uniform convergence, $\mathcal{I}_2$-uniformly Cauchy sequences and $\mathcal{I}_2^*$-uniformly Cauchy sequences for double sequences of functions in $2$-normed spaces. Then, we show the relationships between them.

[1]  E. Dündar,et al.  On $\mathcal{I}$-uniform convergence of sequences of functions in 2-normed spaces , 2020 .

[2]  M. İlkhan.  A new conservative matrix derived by Catalan numbers and its matrix domain in the spaces c and c0 , 2020, Linear and Multilinear Algebra.

[3]  E. Dündar,et al.  $\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces , 2019, Universal Journal of Mathematics and Applications.

[4]  E. Dündar.  ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS , 2015 .

[5]  M. Sen,et al.  I-convergence in probabilistic n-normed space , 2012, Soft Comput..

[6]  S. A. Mohiuddine,et al.  On ideal convergence in probabilistic normed spaces , 2012 .

[7]  M. Mursaleen,et al.  On I-convergence in random 2-normed spaces , 2011 .

[8]  Saeed Sarabadan,et al.  Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces , 2011, Int. J. Math. Math. Sci..

[9]  Pratulananda Das,et al.  I and I*-convergence of double sequences , 2008 .

[10]  Marek Balcerzak,et al.  Statistical convergence and ideal convergence for sequences of functions , 2007 .

[11]  Suna Saltan,et al.  IDEAL CONVERGENCE IN 2-NORMED SPACES , 2007 .

[12]  William H. Ruckle,et al.  Generalized Statistical Convergence and Convergence Free Spaces , 2000 .

[13]  J. A. Fridy,et al.  ON STATISTICAL CONVERGENCE , 1985 .

[14]  I. J. Schoenberg.  The Integrability of Certain Functions and Related Summability Methods , 1959 .

[15]  E. Dündar,et al.  On statistical convergence of sequences of functions in 2-normed spaces , 2017 .

[16]  Fatih Nuray,et al.  the convergence , 2011 .

[17]  Mehmet Gürdal,et al.  On ℐ-Cauchy sequences in 2-normed spaces , 2008 .

[18]  M. Güngör,et al.  Statistical Convergence of Double Sequences of Real-Valued Functions , 2007 .

[19]  S. Gähler,et al.  Lineare 2-normierte Räume† , 1964 .

[20]  S. Gähler,et al.  2-metrische Räume und ihre topologische Struktur†‡‡ , 1963 .

[21]  H. Fast,et al.  Sur la convergence statistique , 1951 .