In the present paper some different types of boundedness in fuzzy normed linear spacesof type x, n. We give the statistically cauchy sequence in neutrosophic. So with this chapter of lang you are moving ahead hundreds of years from newton and leibnitz, perhaps 70 years from riemann. An intuitionisticfuzzynormor in short ifnon v is an object of the form a x. Every finite dimensional f sub space y of a fuzzy normed linear space x is complete. In the following theorem, we investigate fuzzy sequentially continuity of cubic mappings in fuzzy normed spaces. On functions preserving convergence of series in fuzzy. In this paper we continue the study of fuzzy continuous mappings in fuzzy normed linear spaces initiated by t.
A felbinfuzzy normed space x,kk is said to have the lbounded approximation property, brie. Because of the triangle inequality, the function dx. Research article a generalized mazurulam theorem for fuzzy. In this chapter, we define fuzzy normed spaces and show that every fuzzy normed space induces a fuzzy metric space. Then xk is a cauchy sequence in the locally convex topology generated by nif and only if. Stability results in nonarchimedean l fuzzy normed. Indeed, we will show that under some extra conditions on theorem 3. Fibonacci statistical convergence on intuitionistic fuzzy. Because of the cauchyschwarzbunyakowskyinequality, prehilbert spaces are normed spaces, and hilbert spaces are banach spaces.
Pdf in this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced. His research interests center on the fuzzy normed spaces and functional analysis. The approximation property ap is an essential concept in researching functional analysis because the ap has been studied for the shauder basis and operator theory. G vectorspaces in this section we give a brief reminder of vector spaces and associated notions. Finally, section 3 is devoted to introduce limit point, thin subsequence, nonthin subsequence, statistical limit point and statistical cluster point of double sequences in fuzzy normed spaces and. Since then many authors studied some properties of maps and linear operators in these fuzzy normed spaces see eg. In 1992, felbin 3 introduced another concept of fuzzy norm defined on a vector space by putting in correspondence to each element of the linear. Introduction to normed vector spaces audrey terras march 29, 2009 1 why worry about innite dimensional normed vector spaces. I convergence in intuitionistic fuzzy nnormed linear space. In this paper, we study the concept of fibonacci statistical convergence on intuitionisitic fuzzy normed space. Introduction to normed vector spaces ucsd mathematics. Based on the open mapping and closed graph theoremes on these fuzzy metric spaces. We continue our work by coining fuzzy soft normed linear space in a different way as a fuzzy set defined on the soft normed linear space.
In particular every finite dimensional fuzzy normed linear space is complete. We use the definition of fuzzy normed linear spaces to establish a fuzzy version of a generalized hyersulamrassias stability for above equation in the fuzzy normed linear space setting. A study of boundedness in fuzzy normed linear spaces mdpi. We obtain a mazurulam theorem for fuzzy isometry mappings in the strictly convex nonarchimedean fuzzy normed spaces. There has been a systematic development of fuzzy normed linear spaces fnlss and one of the important development over fnls is the notion of intuitionistic fuzzy normed linear space ifnls. We also explore some expected basic properties of these definition 1. Reference 16, we made a comparison study among approximation properties in felbin fuzzy normed spaces with other fuzzy normed spaces. Properties of continuous maps and bounded linear operators. We define the fibonacci statistically cauchy sequences with respect to an intuitionisitic fuzzy normed space and introduce the fibonacci statistical completenes with respect to an intuitionisitic fuzzy normed space. Katsaras, fuzzy topological vector spaces i, fuzzy sets and systems 6. On the mazurulam theorem in nonarchimedean fuzzy normed spaces.
This is why the study of fuzzy normed linear spaces felbins type and samantas type is of great importance. The aim of this paper is to obtain fixed point of mapping satisfying an implicit relation on fuzzy metric spaces. Some remarks on fuzzy n normed spaces 43 theorem 3. The aleksandrov problem in nonarchimedean 2fuzzy 2. A new concept of fuzzy normed space was introduced by saadati and. A fuzzy normed linear space x, i111 is said to be complete if every cauchy sequence see definition 3. Finite dimensional fuzzy normed linear space sciencedirect. We want to understand the integral from langs perspective rather than that of your calculus book. The organization of the paper is as in the following. Fuzzy real number, fuzzy normed linear space, mono tone, solidness, convergence free and symmetricity. Further, a new concept of convergence of sequences in an intuitionistic fuzzy n normed linear space ifnnls was. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed spaces. The main aim of this paper is to consider the fuzzy normed spaces and define the fuzzy banach spaces and also the introduction of fuzzy metric spaces of its quotients and prove some theorems and lemmas with the example.
Then xk is a cauchy sequence in the locally convex topology generated by nif and. On generalized fuzzy normed spaces 1241 it follows that. Some open problems in this framework are mentioned. Until now, it has been widely found outcomes related to fuzzy normed space and fuzzy inner product space. The aleksandrov problem in nonarchimedean 2fuzzy 2normed. Abstract the fundamental aim of this paper is to consider and introduce fuzzy. Bag and samanta introduced a definition of fuzzy norm over a linear space following the definition of cheng and moordeson and they have studied finite dimensional fuzzy normed linear spaces. Therefore the spectrum of the category of fuzzy normed linear spaces is broader than the category of normed spaces. We introduce the definition of intuitionistic fuzzy pseudonorm and study some properties of convergence and. Fuzzy normed linear space and its topological structure. Stability of general cubic mapping in fuzzy normed spaces. N is fuzzy 2 norm on x in the sense that associated to x x and t r, nx 1, x 2, t indicates the truth value of the statement. We introduce the definition of nonarchimedean 2fuzzy 2normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. With these definitio ns, we investigate relations of convergence, s convergence and st convergence in fuzzy normed spaces.
Also the important lebesgue spaces lpw,s,m and the abstract hilbert spaces that we will study later on will be examples of normed spaces. A study of approximation properties in felbinfuzzy normed spaces. Other approaches for fuzzy normed linear spaces can be found in 1, 2, 9. The motivation of this paper is to present a new notion of nonarchimedean fuzzy normed space over a field with valuation. It is seen that this concept, which is very important for reallife situations, had not enough solution to some problems in time. One of the problems in lfuzzy topology is to obtain an appropriate concept of lfuzzy metric spaces and lfuzzy normed spaces. The primary purpose of this paper is to introduce the notion of fuzzy n normed linear space as a generalization of n normed space. Finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces. Finite dimensional fuzzy normed linear space fuzzy sets and. Pdf intuitionistic fuzzy euclidean normed spaces reza. An intuitionisticfuzzynormor in short ifnon v is an object of the form a x, t, n x, t, m x, t. In 2004, park introduced and studied the notion of intuitionistic fuzzy metric spaces. Using fuzzy flterbases, we characterize fuzzy ecompactness and fuzzy eclosed spaces. Intuitionistic fuzzy pseudonormed linear spaces new.
Direct approach to the stability of a cubic functional. Aug, 2018 in this chapter, we define fuzzy normed spaces and show that every fuzzy normed space induces a fuzzy metric space. And then we can get isometry when a mapping satisfies aopp and in article by applying the benzs theorem about the aleksandrov problem in nonarchimedean 2fuzzy 2. Neutrosophic normed spaces and statistical convergence murat kiris. Felbin, finite dimensional fuzzy normed linear space, fuzzy sets and systems 48 1992, 239248. Research article a generalized mazurulam theorem for. Neutrosophic normed spaces and statistical convergence. Let x% be an absolute soft linear space over the scalar field k. Pdf on dec 20, 2018, kyugeun cho and others published on convergences in fuzzy normed spaces find, read and cite all the. Research article on the mazurulam theorem in nonarchimedean.
In this paper, generalized fuzzy norms are defined on a set of objects endowed with a structure of linear space. Fuzzy normed spaces and fuzzy metric spaces springerlink. In this paper we first show that the two notations of fuzzy continuity and topological continuity are equivalent and also prove that fuzzy normed spaces are topological vector spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the. Then we consider the topology induced by fuzzy normed metric spaces and show some important topological properties of them.
Home browse by title periodicals fuzzy sets and systems vol. On fuzzy 2inner product spaces parijat sinha1, ghanshyam lal2 and divya mishra2 1department of mathematics, v. Pdf fuzzy normed space of operators and its completeness. The present thesis consisting of three chapters is devoted to the study of fuzzy topological spaces. Now we examine some conditions under which the cubic mapping found in theorem 3. Approximation properties in felbin fuzzy normed spaces. Also finite dimensional normed fuzzy spaces are consid ered briefly. These approximation properties are new concepts in felbin fuzzy normed spaces. The concept of a fuzzy normed linear space is introduced.
Statistical convergence of double sequences in fuzzy normed. An example of a fuzzy normed space which is not a normed. We introduce the definition of nonarchimedean 2 fuzzy 2 normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. The theory of such normed vector spaces was created at the same time as quantum mechanics the 1920s and 1930s. Abstractfollowing the concept of fuzzy norm introduced by t. It is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence. Index terms 2normed spaces, nnormed spaces, fuzzy normed spaces. It has been proven in 6 that every n normed space is a normed space and in and 12 has also been demonstrated that the normed space. Some properties of twofuzzy nor med spaces iosr journal. Liu, fuzzy vector spaces and fuzzy topological vector spaces, journal of mathematical analysis and applications 58 1977, 5146. Index terms 2 normed spaces, n normed spaces, fuzzy normed spaces. Weak fuzzy topology on fuzzy topological vector spaces. Finite dimensional fuzzy normed linear space fuzzy sets.
Ideal convergence in 2fuzzy 2normed spaces mohammad h. Properties of continuous maps and bounded linear operators in. Next, we study fuzzy inner product spaces and some properties of these spaces. Next, a hahnbanach theorem for weakly fuzzy bounded linear functional with some of its. A study of approximation properties in felbinfuzzy normed. Reza saadati received his bs and ms from yazd university under the direction of professor s. It has been proven in 6 that every nnormed space is a normed space and in and 12 has also been demonstrated that the normed space. On fuzzy 2inner product spaces research india publications. On the mazurulam theorem in nonarchimedean fuzzy normed. Pdf a study of boundedness in fuzzy normed linear spaces.
When the space v is complete with respect to this metric, v is a banach space. Research article a generalized mazurulam theorem for fuzzy normed spaces j. Stability of general cubic mapping in fuzzy normed spaces in. On generalized fuzzy normed spaces including function mehmet kir, mehmet acikgoz.
Xiscalledafuzzy normed linear spacevalued sequence space. Afterwards, beg and abbas, vasuki, popa, and imad et al. In this paper, we prove the ulamhyers stability of the cubic functional equation. Stabilities of cubic mappings in fuzzy normed spaces. Statistical convergence of double sequences in fuzzy. In this paper, a common fixed point theorem for a pair of operators in fuzzy normed spaces is established.