Statistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function

Abstract

The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study convergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.

LACUNARY I-CONVERGENT AND LACUNARY I-BOUNDED SEQUENCE SPACES DEFINED BY AN ORLICZ FUNCTION Vol. 4(2) July. 2016, No. 14, pp. 150-159 EMRAH EVREN KARA, MERVE ILKHAN

“…then the sequence x = (x i ) is said to be lacunary I-convergent to l and lacunary I-null, respectively. It can be seen in [9,11,23,24,39,45], the authors used the concept of ideal convergence and lacunary sequence to define different types of sequence spaces.…”

A New Double Sequence Space m2(F,ϕ,p) Defined by a Double Sequence of Modulus Functions

“…The double sequence spaces in the various forms were introduced and studies by Khan and Tabassum in [7][8][9][10][11][12][13][14], by Khan in [15], and by Khan et al in [16,17]. Now let be a family of subsets having most elements in N. Also , denote the class of subsets = 1 × 2 in N × N such that the elements of 1 and 2 are most and , respectively.…”

On a New Space of Double Sequences

“…, , and its convergence implies the convergence by | ⋅ | of partial sums sequence { , }, where , = ∑ =1 ∑ =1 , (see [1][2][3][4]).…”

“…The space ℓ is closely related to the space ℓ , which is an Orlicz sequence space with ( ) = for 1 ≤ < ∞. The double sequence spaces in the various forms defined by Orlicz functions were introduced and studied by Khan and Tabassum in [6][7][8][9][10][11][12] and by Khan et al in [13].…”