On ideal convergence of double sequences in 2-fuzzy n-normed linear space

The purpose of this paper is to define the notions of convergence, Cauchy st–convergence, st–Cauchy, I –convergence and I –Cauchy for double sequences in 2–fuzzy n–normed spaces with respect to α–n–norms and study certain classical and standard properties related to these notions.

On Some <i>I</i>-Convergent Double Sequence Spaces Defined by a Modulus Function

In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces and ,for a modulus function f and study some of the properties of these spaces.

I-Pre-Cauchy Double Sequences and Orlicz Functions

Let be a double sequence and let M be a bounded Orlicz function. We prove that x is I-pre-Cauchy if and only if This implies a theorem due to Connor, Fridy and Klin [1], and Vakeel A. Khan and Q. M. Danish Lohani [2]

Some I-Convergent Sequence Spaces Defined by Orlicz Functions

In this article we introduce the sequence spaces cI（M）, c0I（M）, mI（M） and m0I（M） using the Orlicz function M. We study some of the properties like solid, symmetric, sequence algebra, etc and prove some inclusion relations.

Vitali Type Convergence Theorems for Banach Space Valued Integrals

Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergence