In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.

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Lacunary Statically Convergent and Lacunary Strongly Convergent Generalized Difference Sequences of Fuzzy Real Numbers

λ-Difference sequence spaces of fuzzy numbers

The purpose of this paper is to introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences of fuzzy numbers. We give some relations related to these concepts. We show that lacunary @D^m-statistical convergence and lacunary strongly @D"("p")^m-convergence are equivalent for @D^m-bounded sequences of fuzzy numbers. We also introduce the concept of lacunary @D^m-statistically Cauchy sequence and show that it is equivalent to the lacunary @D^m-statistical convergence.

Lacunary Statistical and Lacunary Strongly Convergence of Generalized Difference Sequences of Fuzzy Numbers

The idea of difference sequences of real (or complex) numbers was generalized by Et and Colak [Et M, Colak R. On some generalized difference sequence spaces. Soochow J Math 1995; 21(4): 377–86; Colak R, Et M. On some generalized difference sequence spaces and related matrix transformations. Hokkaido Math J 1997; 26(3): 483–92]. In this paper, using the difference operator Δ m and an Orlicz function, we introduce and examine some sequence spaces of fuzzy numbers. We study some of their properties like completeness, solidity, symmetricity, etc. We also give some relations related to these spaces.

Generalized difference sequences of fuzzy numbers

The idea of difference sequences of real (or complex) numbers was generalized by Et and Colak (9). In this paper, using the difference operator ∆ m and an Orlicz function, we introduce and examine a class of sequences of fuzzy numbers. We study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to this class.

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On a class of fuzzy sets defined by Orlicz functions

In this paper, we work on the structure of soft linear spaces over a field K and investigate some of its properties. Here, we use the concept of the soft point which was introduced in [2, 6]. We then introduce the soft norm in soft linear spaces. Finally, we examine the properties of this soft normed space and present some investigations about soft continuous operators in the space.

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A New View on Soft Normed Spaces

The main object of the paper is to study the inclusions [Aσ, p]⊂[Aσ, q], [Aσ, p]⊂[Bσ, q] and [Aσ, p]∩m⊂[Bσ, q] and to characterizae the spaces M([Aσ, p], [Aσ, q]) and M0([Aσ, p]0, [Aσ, q]0). Here [Aσ, p] and [Aσ, q]0 are certain spaces of strongly summable sequences in terms of an injection σ: N→N and anonnegative infinite matrix A, and M([Aσ, p], [Aσ, q]) is the space of summability factors between [Aσ, p] and [Aσ, q].

Note on strong Aσ-summability

Lacunary strong A-convergence with respect to a sequence of modulus functions

In this paper we introduce new sequence space $m(M,A,\phi ,p)$ defined by combining an Orlicz function and an infinite matrix. We study its different properties and obtain some inclusion relations involving the space $m(M,A,\phi ,p)$.

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Tunay Bilgin

Papers

A New View on Soft Normed Spaces

Note on strong Aσ-summability

Lacunary strong A-convergence with respect to a sequence of modulus functions

On a new class of sequences related to the

Lacunary strongly Δ-convergent sequences of fuzzy numbers