INTEGRATED RATE SPACE ∫ ℓ<sub>π</sub>

Subramanian, N.; Rao, K. Chandrasekhara; Gurumoorthy, N.

doi:10.4134/ckms.2007.22.4.527

Cited by 2 publications

(4 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Subramanian et.al. [5] gave the integrated rate space ∫ ℓ π and studied some properties of this space. And they also characterized the matrix classes ( In this paper, we proved that the integrated and differentiated sequence spaces are Banach spaces, BK−spaces and norm isomorphic to ℓ 1 .…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Integrated and Differentiated Sequence Spaces

Kirişçi¹

2015

Journal of Nonlinear Analysis and Application

View full text Add to dashboard Cite

In this paper, we investigate integrated and differentiated sequence spaces which emerge from the concept of the sequence space ℓ 1 . The integrated and differentiated sequence spaces were initiated by Goes and Goes [4]. The main propose of the present paper, we study matrix domains and some properties of the integrated and differentiated sequence spaces. In Section 3, we compute the alpha-, beta-and gamma duals of these spaces. Afterward, we characterize the matrix classes of these spaces with well-known sequence spaces.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Subramanian et.al. [5] gave the integrated rate space ℓ π and studied some properties of this space. And they also characterized the matrix classes ℓ π : Y , where Y = {ℓ ∞ , c, c 0 , ℓ p , bv, bv 0 , bs, cs, ℓ ρ , ℓ π }.…”

Section: Discussionmentioning

confidence: 99%

Integrated and Differentiated Sequence Spaces

Kirişçi¹

2015

Journal of Nonlinear Analysis and Application

View full text Add to dashboard Cite

show abstract

“…The integrated and differentiated sequence spaces were initiated by Goes and Goes [2]. Subramanian et al [9] gave the integrated rate space and studied some properties. Until Kirişci paper [3], there was no work on differentiated sequence spaces.…”

Section: Preliminaries Background and Notationmentioning

confidence: 99%

“…In Goes & Goes [4], some properties related to the integrated space were studied, but the properties related to the differentiated spaces were not given. The integrated rate space is defined and investigated some properties by Subramanian et al [11]. Kirişci [5] defined new integrated and differentiated spaces by using the new Ω and Γ matrices.…”

Section: Introductionmentioning

confidence: 99%

Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Kirişçi¹

2017

Fasciculi Mathematici

View full text Add to dashboard Cite

Abstract. Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Fuzzy sets have become popular in every branch of mathematics such as analysis, topology, algebra, applied mathematics etc. Thus fuzzy sets triggered the creation of a wide range of research topics in all areas of science in a short time. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Key words: fuzzy numbers, integrated matrix, differentiated matrix, real duals.AMS Mathematics Subject Classification: 03E72, 46A45, 40C05. IntroductionFuzziness has revolutionized many areas such as mathematics, science, engineering, medicine. This concept was initiated by Zadeh [17]. Not only Zadeh discovered this concept, but he also developed the infrastructure of today's popular forms of use such as relations of similarity, decision making, and fuzzy programming in a short time.Just like in the theory of sets, fuzzy sets(FS) also have led to the emergence of new mathematical concepts, research topics, and the design of engineering applications. Therefore, the nature of the classical set theory must be well known and understood. In particular, consider the two fundamental laws of Boolean algebra the law of excluded middle and law of contradiction. In logic, the proposition every proposition is either true or falseť excludes any third, or middle, possibility, which gave this principle the name of the law of excluded middle. When look at the principles of Boolean algebra, there are two items as prediction: "True" or "False". Whether classical, Unauthenticated Download Date | 5/9/18 6:25 PM 76Murat Kirişci Boolean or crisp, set theory can be defined as a characteristic function of the membership of an element x in a set A. For each elements of universal set X, the function that generates the values 0 and 1 is called the characteristic function.Today, the studies and applications related to the fuzziness are increasing rapidly and this concept is finding in every scientific areas. Zadeh's FS theory succeeded in attracting mathematicians as well as other scientists and was adopted. The most important feature of FS is to generalize the values of "true" and "false" in traditional logic and to produce a logic that can use multi-valued results.Any change or transition in real life takes place between membership and non-membership. This transition is clear, well-defined. Despite this certainty in classical sets, this is somewhat different in FS. This difference arises because the transition is gradual. The uncertainty of the boundaries of the FS implies that this transition will vary from one membership to another. In that case, membership of an element from the universe in this set is measured by a function that attempts to describe vagueness and ambiguity.Matlok...

show abstract

INTEGRATED RATE SPACE ∫ ℓ_π

Cited by 2 publications

References 1 publication

Integrated and Differentiated Sequence Spaces

Integrated and Differentiated Sequence Spaces

Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Contact Info

Product

Resources

About

INTEGRATED RATE SPACE ∫ ℓπ

Cited by 2 publications

References 1 publication

Integrated and Differentiated Sequence Spaces

Integrated and Differentiated Sequence Spaces

Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Contact Info

Product

Resources

About

INTEGRATED RATE SPACE ∫ ℓ_π