Bipan Hazarika

Paranorm I-convergent sequence spaces

In this article we introduced the sequence spaces cI(p), c0I(p), mI(p) and m0I(p) for p = (pk), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations.

IDEAL QUASI-CAUCHY SEQUENCES

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. A sequence (xn) of real numbers is said to be I-convergent to a real number L if for each ε>0, the set {n:|xn−L|≥ε} belongs to I. We introduce I-ward compactness of a subset of R, the set of real numbers, and I-ward continuity of a real function in the senses that a subset E of R is I-ward compact if any sequence (xn) of points in E has an I-quasi-Cauchy subsequence, and a real function is I-ward continuous if it preserves I-quasi-Cauchy sequences where a sequence (xn) is called to be I-quasi-Cauchy when (Δxn) is I-convergent to 0. We obtain results related to I-ward continuity, I-ward compactness, ward continuity, ward compactness, ordinary compactness, ordinary continuity, δ-ward continuity, and slowly oscillating continuity.MSC: 40A35, 40A05, 40G15, 26A15.

I-MONOTONIC AND I-CONVERGENT SEQUENCES

In this article we study the noton of I-monotonic sequences. We prove the decomposition theorem and generalize some of the results on monotonic sequences. We also introduce I-convergent series and studied some results.

Lacunary I-Convergent Sequences

In this article we introduce the concepts of lacunary I-convergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.

Fuzzy real valued lacunary I-convergent sequences

Abstract In this article, we introduce the concept of lacunary I -convergent sequence of fuzzy real numbers and study some basic properties.

Some I-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz functions

Abstract In this paper we introduce certain new sequence spaces of fuzzy numbers defined by I -convergence using sequences of Orlicz functions and a difference operator of order m . We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces.

Lacunary difference ideal convergent sequence spaces of fuzzy numbers

In this article, using the Orlicz function M and the difference operator of order n ≥ 1, we introduce the spaces of lacunary ideal convergent difference sequences and lacunary strongly summable difference sequences of fuzzy numbers via fuzzy metric. We also established some relations related to these spaces. Further, we study some basic topological properties of these spaces.

λ-ideal convergence in intuitionistic fuzzy 2-normed linear space

An ideal I is a family of subsets of positive integers

On σ-uniform density and ideal convergent sequences of fuzzy real numbers

\mathbb{N}

On fuzzy real valued generalized difference I-convergent sequence spaces defined by Musielak-Orlicz function

which is closed under taking finite unions and subsets of its elements. In [8], Kostyrko et al., introduced the concept of ideal convergence as a sequence xk of real numbers is said to be I-convergent to a real number