scholarly journals On Certain Topological Properties of Normed Space Valued Null Function Space c0 (S, (E, || . || ), xi, u) and Its Paranormed Structure

2015 ◽  
Vol 15 (1) ◽  
pp. 121-128
Author(s):  
Narayan Prasad Pahari
Keyword(s):  
Functional Analysis ◽  
Function Space ◽  
Normed Space ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Basic Sequence ◽  
Topological Properties ◽  
New Class ◽  
And Function ◽  
Class Of Functions

The aim of this paper is to introduce and study a new class c0 (S, (E, || . || ), ξ, u) of normed space E valued functions which will generalize some of the well known  basic sequence spaces and function spaces studied in Functional Analysis.. Beside the investigation pertaining to the linear paranormed structure of the class c0 ( S, (E, || . || ), ξ, u ) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class c0 (S, (E, || . || ), ξ, u) in terms of different ξ and u so that such a class of functions is contained in or equal to another class of similar nature.DOI: http://dx.doi.org/10.3126/njst.v15i1.12028Nepal Journal of Science and TechnologyVol. 15, No.1 (2014) 121-128

Generalized Sequence Spaces in 2-Normed Spaces Defined by Ideal and a Modulus Function

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudhir Kumar ◽  
Vijay Kumar ◽  
S.S. Bhatia
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Topological Properties ◽  
Normed Spaces ◽  
New Class ◽  
Difference Sequences ◽  
Convergent Sequences

AbstractThe main objective of this paper is to define some new kind of generalized convergent sequence spaces with respect to a modulus function, and difference operator Δm, m ≥ 1 in a 2-normed space. We also examine some topological properties of the resulting sequence spaces. Finally, we have introduced a new class of generalized convergent sequences with the help of an ideal and difference sequences in the same space.

scholarly journals On Locally Convex Topological Vector Space Valued Null Function Space c0 Defined by Semi Norm and Orlicz Function

2015 ◽  
Vol 19 (1) ◽  
pp. 62-68
Author(s):  
Narayan Prasad Pahari
Keyword(s):  
Vector Space ◽  
Function Space ◽  
Topological Vector Space ◽  
Convex Space ◽  
Orlicz Function ◽  
Locally Convex Space ◽  
New Class ◽  
And Function ◽  
Locally Convex ◽  
Class Of Functions

The aim of this paper is to introduce and study a new class c0 (S, T, Phi, Xi, u) of locally convex space T- valued functions using Orlicz function Phi as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the structures of the class c0 (S, T, Phi, Xi, u), our primarily interest is to explore some of the containment relations of the class c0 (S, T, Phi, Xi, u) in terms of different Xi and u so that such a class of functions is contained in or equal to another class of similar nature.Journal of Institute of Science and Technology, 2014, 19(1): 62-68

scholarly journals On Locally Convex Topological Vector Space Valued Paranormed Function Space Defined by Orlicz Function

2014 ◽  
Vol 14 (2) ◽  
pp. 109-116
Author(s):  
NP Pahari
Keyword(s):  
Vector Space ◽  
Function Space ◽  
Convex Space ◽  
Orlicz Function ◽  
Locally Convex Space ◽  
Similar Nature ◽  
New Class ◽  
And Function ◽  
Locally Convex ◽  
Class Of Functions

The aim of this paper is to introduce and study a new class (l∞ (X, Y, Φ, ξ, w , L), HU) of locally convex space Y- valued functions using Orlicz function Φ as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the linear topological structures of the class (l∞ (X, Y, Φ, ξ, w , L), HU) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class l∞ (X, Y, Φ, ξ, w) in terms of different ξ and w so that such a class of functions is contained in or equal to another class of similar nature. DOI: http://dx.doi.org/10.3126/njst.v14i2.10423   Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 109-116

scholarly journals Some remarks on functions with values in probabilistic normed spaces

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
Ioan Goleţ
Keyword(s):  
Normed Space ◽  
Topological Properties ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Random Functions ◽  
New Class ◽  
Probabilistic Normed Spaces ◽  
Special Cases ◽  
Probabilistic Norm

AbstractIn this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.

scholarly journals Duals of vector-valued Köthe function spaces

1992 ◽  
Vol 112 (1) ◽  
pp. 165-174 ◽  
Author(s):  
Miguel Florencio ◽  
Pedro J. Paúl ◽  
Carmen Sáez
Keyword(s):  
Function Space ◽  
Normed Space ◽  
Function Spaces ◽  
Integrable Functions ◽  
Nikodym Property ◽  
Köthe Dual ◽  
Vector Valued

AbstractLet Λ be a perfect Köthe function space in the sense of Dieudonné, and Λ× its Köthe-dual. Let E be a normed space. Then the topological dual of the space Λ(E) of Λ-Bochner integrable functions equals the corresponding Λ×(E′) if and only if E′ has the Radon–Nikodým property. We also give some results concerning barrelledness for spaces of this kind.

scholarly journals Quasi cl-supercontinuous functions and their function spaces

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
J. K. Kohli ◽  
Jeetendra Aggarwal
Keyword(s):  
Continuous Functions ◽  
Function Spaces ◽  
Strong Form ◽  
General Topology ◽  
Regular Space ◽  
Basic Properties ◽  
New Class ◽  
Mathematical Literature ◽  
Class Of Functions ◽  
Appl Math

AbstractA new class of functions called ‘quasi cl-supercontinuous functions’ is introduced. Basic properties of quasi cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the mathematical literature is elaborated. The notion of quasi cl-supercontinuity, in general, is independent of continuity but coincides with cl-supercontinuity (≡ clopen continuity) (Applied General Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772), a significantly strong form of continuity, if range is a regular space. The class of quasi cl-supercontinuous functions properly contains each of the classes of (i) quasi perfectly continuous functions and (ii) almost cl-supercontinuous functions; and is strictly contained in the class of quasi

scholarly journals New Difference Sequence Spaces Defined by Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
S. A. Mohiuddine ◽  
A. Kılıçman
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

Abstract Köthe spaces. IV

1968 ◽  
Vol 64 (1) ◽  
pp. 45-52
Author(s):  
D. H. Fremlin
Keyword(s):  
Tensor Product ◽  
Function Space ◽  
Function Spaces ◽  
Riesz Space ◽  
Natural Order ◽  
Order Structure ◽  
Topological Properties ◽  
Projective Tensor Product ◽  
Köthe Spaces ◽  
Projective Tensor

In this paper I investigate the completed projective tensor product of two perfect Riesz spaces, and show how a natural order structure on this renders it also a perfect Riesz space. Sections 7–14 contain interesting order-topological properties of this tensor product. Finally, section 15 describes how the tensor product of function spaces may be represented as a function space, in the manner of (1 b).

scholarly journals New Sequence Spaces and Function Spaces on Interval[0,1]

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Cheng-Zhong Xu ◽  
Gen-Qi Xu
Keyword(s):  
Banach Spaces ◽  
Function Spaces ◽  
Summation Method ◽  
Sequence Spaces ◽  
Polynomial Space ◽  
And Function

We study the sequence spaces and the spaces of functions defined on interval0,1in this paper. By a new summation method of sequences, we find out some new sequence spaces that are interpolating into spaces betweenℓpandℓqand function spaces that are interpolating into the spaces between the polynomial spaceP0,1andC∞0,1. We prove that these spaces of sequences and functions are Banach spaces.

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