Some new classes of paranorm ideal convergent double sequences of sigma-bounded variation over n-normed spaces

Rough Convergence of Double Sequences in $n-$Normed Spaces

“…Later, many researchers used double sequences in their works in the area of summability theory. This work can be found in [27][28][29][30][31][32]. Malik and Maity [33] defined and exaimed rough convergence of double sequences, the set of r−limit points of double sequences and rough Cauchy double sequences.…”

“…Currently, we recall the idea of n−normed spaces, some fundamental definitions, and notations. (See [8,10,11,30,33,37]). Definition 1.1.…”

“…, • ) is said to be bounded if there exists a nonnegative real number M such that x tk , z 2 , • • • , z n < M for all t, k ∈ N. Definition 1.7. [30] A double sequence (x tk ) in n−normed space (X, •, •, . .…”

On Tribonacci I -convergent sequence spaces

“…Furthermore, some authors also investigated it from the sequence space point of view. For more details on I-convergence, we refer to [2,11,13,14,18,25,27,33].…”

On i-convergent sequence spaces defined by Jordan totient operator

“…Afterward, the notion of ideal convergence or simply I-convergence was moreover explored from the view point of sequence spaces and connected to the theory of summability by Šalát et al [24], Khan and Nazneen [13], Khan et al [15,28], Filip ów and Tryba [5], and many others. For further details about the ideal convergence we refer the reader to [11,12,14,27] and its references.…”