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Journal articles on the topic 'Normed linear spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Barnes, Benedict, I. A. Adjei, S. K. Amponsah, and E. Harris. "Product-Normed Linear Spaces." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 740–50. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3284.

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In this paper, both the product-normed linear space $P-NLS$ (product-Banach space) and product-semi-normed linear space (product-semi-Banch space) are introduced. These normed linear spaces are endowed with the first and second product inequalities, which have a lot of applications in linear algebra and differential equations. In addition, we showed that $P-NLS$ admits functional properties such as completeness, continuity and the fixed point.

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2

REN, GUANSHEN. "Nonarchimedean Normed Linear Spaces." Annals of the New York Academy of Sciences 659, no. 1 Papers on Gen (September 1992): 163–71. http://dx.doi.org/10.1111/j.1749-6632.1992.tb32259.x.

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3

Narita, Keiko, Noboru Endou, and Yasunari Shidama. "Bidual Spaces and Reflexivity of Real Normed Spaces." Formalized Mathematics 22, no. 4 (December 1, 2014): 303–11. http://dx.doi.org/10.2478/forma-2014-0030.

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Summary In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals as linear operators by this definition. Accordingly we proved Uniform Boundedness Theorem for linear functionals using the theorem (5) from [21]. Finally, we defined reflexivity of real normed spaces and proved some theorems about isomorphism of linear operators. Using them, we proved some properties about reflexivity. These formalizations are based on [19], [20], [8] and [1].

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4

Ettayb, J. "Some results on ultrametric 2-normed spaces." Researches in Mathematics 32, no. 1 (July 8, 2024): 45. http://dx.doi.org/10.15421/242404.

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In this paper, we study the ultrametric 2-normed spaces and the ultrametric 2-Banach spaces. In particular, we establish some results on Cauchy sequences in ultrametric 2-normed spaces. Also, we introduce and study the notion of bounded linear 2-functionals on ultrametric 2-Banach spaces and we give some of its properties. On the other hand, the new norm on the ultrametric 2-normed space is constructed. The concepts of closed operators between ultrametric 2-normed spaces and $b$-linear functionals in ultrametric 2-normed spaces are introduced. Finally, a necessary and sufficient condition for a linear operator to be closed in terms of its graph is proved and some results on bounded $b$-linear functionals in ultrametric 2-normed spaces are given.

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5

Roy, Ranajoy, Sujoy Das, and S. K. Sam anta. "On Multi Normed Linear Spaces." International Journal of Mathematics Trends and Technology 48, no. 2 (August 25, 2017): 111–19. http://dx.doi.org/10.14445/22315373/ijmtt-v48p514.

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6

Watson, G. A. "Approximation in normed linear spaces." Journal of Computational and Applied Mathematics 121, no. 1-2 (September 2000): 1–36. http://dx.doi.org/10.1016/s0377-0427(00)00333-2.

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7

Godini, G. "On normed almost linear spaces." Mathematische Annalen 279, no. 3 (January 1988): 449–55. http://dx.doi.org/10.1007/bf01456281.

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8

Sejeeni, Fowzi Ahmad, and Matooq Ahmad Badri. "The moment spaces of normed linear spaces." Bulletin of the Australian Mathematical Society 45, no. 2 (April 1992): 277–83. http://dx.doi.org/10.1017/s0004972700030148.

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For a linearly independent sequence in a normed linear space the moment space is defined. Basic properties of moment spaces are discussed as well as a necessary and sufficient condition for the moment space to be a closed subspace of l∞.

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9

Bouadjila, K., A. Tallab, and E. Dahia. "Banach-Steinhaus theorem for linear relations on asymmetric normed spaces." Carpathian Mathematical Publications 14, no. 1 (June 30, 2022): 230–37. http://dx.doi.org/10.15330/cmp.14.1.230-237.

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We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces.

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10

Khan, Vakeel A., Ayhan Esi, Mobeen Ahmad, and Mohammad Daud Khan. "Continuous and bounded linear operators in neutrosophic normed spaces." Journal of Intelligent & Fuzzy Systems 40, no. 6 (June 21, 2021): 11063–70. http://dx.doi.org/10.3233/jifs-202189.

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In this article, we show that the addition and scalar multiplication in neutrosophic normed spaces are continuous. The neutrosophic boundedness and continuity of linear operators between neutrosophic normed spaces are examined. Moreover, we analyzed that the set of all neutrosophic continuous linear operators and the set of all neutrosophic bounded linear operators from neutrosophic normed spaces into another are vector spaces.

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11

Nakasho, Kazuhisa, Yuichi Futa, and Yasunari Shidama. "Continuity of Bounded Linear Operators on Normed Linear Spaces." Formalized Mathematics 26, no. 3 (October 1, 2018): 231–37. http://dx.doi.org/10.2478/forma-2018-0021.

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Summary In this article, using the Mizar system [1], [2], we discuss the continuity of bounded linear operators on normed linear spaces. In the first section, it is discussed that bounded linear operators on normed linear spaces are uniformly continuous and Lipschitz continuous. Especially, a bounded linear operator on the dense subset of a complete normed linear space has a unique natural extension over the whole space. In the next section, several basic currying properties are formalized. In the last section, we formalized that continuity of bilinear operator is equivalent to both Lipschitz continuity and local continuity. We referred to [4], [13], and [3] in this formalization.

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12

Álvarez, Teresa. "Linear relations on hereditarily indecomposable normed spaces." Bulletin of the Australian Mathematical Society 74, no. 2 (October 2006): 289–300. http://dx.doi.org/10.1017/s0004972700035723.

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We introduce the notion of hereditarily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular linear relations. We also show that if X is a complex hereditarily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as λI + S, where λ ∈ ℂ and S is a strictly singular linear relation.

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13

Ma, Yumei. "Isometry on Linear n-G-quasi Normed Spaces." Canadian Mathematical Bulletin 60, no. 2 (June 1, 2017): 350–63. http://dx.doi.org/10.4153/cmb-2016-061-9.

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AbstractThis paper generalizes the Aleksandrov problem: the Mazur-Ulam theoremon n-G-quasi normed spaces. It proves that a one-n-distance preserving mapping is an n-isometry if and only if it has the zero-n-G-quasi preserving property, and two kinds of n-isometries on n-G-quasi normed space are equivalent; we generalize the Benz theorem to n-normed spaces with no restrictions on the dimension of spaces.

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14

Nakasho, Kazuhisa. "Transformation Tools for Real Linear Spaces." Formalized Mathematics 30, no. 2 (July 1, 2022): 93–98. http://dx.doi.org/10.2478/forma-2022-0008.

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Summary This paper, using the Mizar system [1], [2], provides useful tools for working with real linear spaces and real normed spaces. These include the identification of a real number set with a one-dimensional real normed space, the relationships between real linear spaces and real Euclidean spaces, the transformation from a real linear space to a real vector space, and the properties of basis and dimensions of real linear spaces. We referred to [6], [10], [8], [9] in this formalization.

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15

DALES, H. G., and MOHAMMAD SAL MOSLEHIAN. "STABILITY OF MAPPINGS ON MULTI-NORMED SPACES." Glasgow Mathematical Journal 49, no. 2 (May 2007): 321–32. http://dx.doi.org/10.1017/s0017089507003552.

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AbstractIn this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers–Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

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16

Nakasho, Kazuhisa. "Bilinear Operators on Normed Linear Spaces." Formalized Mathematics 27, no. 1 (April 1, 2019): 15–23. http://dx.doi.org/10.2478/forma-2019-0002.

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Summary The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space. In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.

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17

Charatonik, Włodzimierz J., Alicja Samulewicz, and Roman Wituła. "Limit sets in normed linear spaces." Colloquium Mathematicum 147, no. 1 (2017): 35–42. http://dx.doi.org/10.4064/cm6868-5-2016.

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18

Ma, Yumei. "Isometry on linear n-normed spaces." Annales Academiae Scientiarum Fennicae Mathematica 39 (July 2014): 973–81. http://dx.doi.org/10.5186/aasfm.2014.3941.

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19

Sookoo, Norris. "F-normed spaces and linear operators." Journal of Interdisciplinary Mathematics 24, no. 4 (May 19, 2021): 911–19. http://dx.doi.org/10.1080/09720502.2020.1826628.

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20

Phu, Hoang Xuan. "ROUGH CONVERGENCE IN NORMED LINEAR SPACES." Numerical Functional Analysis and Optimization 22, no. 1-2 (March 31, 2001): 199–222. http://dx.doi.org/10.1081/nfa-100103794.

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21

An, PhanThanh, and Nguyen Ngoc Hai. "δ-Convexity in Normed Linear Spaces." Numerical Functional Analysis and Optimization 25, no. 5-6 (January 2004): 407–22. http://dx.doi.org/10.1081/nfa-200041716.

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22

Dragomir, Sever S., Dan Comǎnescu, and Eder Kikianty. "Torricellian points in normed linear spaces." Journal of Inequalities and Applications 2013, no. 1 (2013): 258. http://dx.doi.org/10.1186/1029-242x-2013-258.

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23

Fischer, Thomas. "Strong unicity in normed linear spaces." Numerical Functional Analysis and Optimization 11, no. 3-4 (January 1990): 255–66. http://dx.doi.org/10.1080/01630569008816374.

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24

Hattori, Yasunao, and Hideki Tsuiki. "Hyperbolic topology of normed linear spaces." Topology and its Applications 157, no. 1 (January 2010): 77–82. http://dx.doi.org/10.1016/j.topol.2009.04.047.

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25

Zheng, Liu, and Zhuang Ya-Dong. "K-rotund complex normed linear spaces." Journal of Mathematical Analysis and Applications 146, no. 2 (March 1990): 540–45. http://dx.doi.org/10.1016/0022-247x(90)90323-8.

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26

Krishna, S. V., and K. K. M. Sarma. "Separation of fuzzy normed linear spaces." Fuzzy Sets and Systems 63, no. 2 (April 1994): 207–17. http://dx.doi.org/10.1016/0165-0114(94)90351-4.

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27

Alonso, Javier, and Carlos Benítez. "Area orthogonality in normed linear spaces." Archiv der Mathematik 68, no. 1 (February 1997): 70–76. http://dx.doi.org/10.1007/pl00000397.

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28

Kavyasree, P. R., and B. Surender Reddy. "Cubic $Gamma$-$n$ normed linear spaces." Malaya Journal of Matematik 06, no. 03 (October 1, 2018): 643–47. http://dx.doi.org/10.26637/mjm0603/0028.

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29

Lim, Teck-Cheong. "Pseudo-Convergence in Normed Linear Spaces." Rocky Mountain Journal of Mathematics 21, no. 3 (September 1991): 1057–70. http://dx.doi.org/10.1216/rmjm/1181072929.

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30

Dinda, Bivas, Santanu Kumar Ghosh, and T. K. Samanta. "Intuitionistic Fuzzy Pseudo-Normed Linear Spaces." New Mathematics and Natural Computation 15, no. 01 (December 25, 2018): 113–27. http://dx.doi.org/10.1142/s1793005719500078.

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31

Rădulescu, Sorin, Diana-Olimpia Alexandrescu, and Vicenţiu D. Rădulescu. "Facility location in normed linear spaces." Optimization Letters 9, no. 7 (January 17, 2015): 1353–69. http://dx.doi.org/10.1007/s11590-015-0846-y.

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32

Freese, Raymond W., Charles R. Diminnie, and Edward Z. Andalafte. "Angle Bisectors in Normed Linear Spaces." Mathematische Nachrichten 131, no. 1 (1987): 167–73. http://dx.doi.org/10.1002/mana.19871310115.

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33

Ha, Ki Sik, Yeol Je Cho, Seong Sik Kim, and M. S. Khan. "Strictly Convex Linear 2-Normed Spaces." Mathematische Nachrichten 146, no. 1 (1990): 7–16. http://dx.doi.org/10.1002/mana.19901460102.

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34

Shahen M. Ali and Laith K. Shaakir. "On S-normed spaces." Tikrit Journal of Pure Science 24, no. 4 (August 4, 2019): 82–86. http://dx.doi.org/10.25130/tjps.v24i4.405.

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The study focused on expanding the concept of 2-normed spaces by developing a new definition ( -normed space), and the study concentrated on the convergent of sequences and Cauchy sequences in our definition, as well as some other branches such as linear transformation and contraction.

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35

ZHU, YUANGUO. "ON PARA-NORMED SPACE WITH FUZZY VARIABLES BASED ON EXPECTED VALUED OPERATOR." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 01 (February 2008): 95–106. http://dx.doi.org/10.1142/s0218488508005066.

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Fuzzy variables are functions from credibility spaces to the set of real numbers. The set of fuzzy variables is a linear space with the classic operations of addition and multiplication by numbers. Its subspace formed by fuzzy variables with finite pth absolute moments is showed to be a complete para-normed space. The concept of para-normed space is novel, and is an extension of normed space. It is seen that most properties of normed spaces hold in para-normed spaces. Also some useful inequalities in para-normed spaces are obtained.

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36

M. Ali, Shahen, and Laith K. Shaakir. "On S-normed spaces." Tikrit Journal of Pure Science 24, no. 4 (August 4, 2019): 82. http://dx.doi.org/10.25130/j.v24i4.851.

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The study focused on expanding the concept of 2-normed spaces by developing a new definition ( -normed space), and the study concentrated on the convergent of sequences and Cauchy sequences in our definition, as well as some other branches such as linear transformation and contraction. http://dx.doi.org/10.25130/tjps.24.2019.078

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37

Astaneh, Ali Ansari. "Completeness of normed linear spaces admitting centers." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 39, no. 3 (December 1985): 360–66. http://dx.doi.org/10.1017/s1446788700026136.

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AbstractIt is shown that a normed linear space admitting (Chebyshev) centers is complete. Then the ideas in the proof of this fact are used to show that every incomplete CLUR (compactly locally uniformly rotund) normed linear space contains a closed bounded convex subset B with the following properties: (a)Bdoes not contain any farthest point; (b)Bdoes not contain any nearest point (to the elements of its complement).

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38

Inoué, Takao, Noboru Endou, and Yasunari Shidama. "Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces." Formalized Mathematics 18, no. 4 (January 1, 2010): 207–12. http://dx.doi.org/10.2478/v10037-010-0025-7.

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Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces In this article, we define and develop differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [16] and [17]).

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39

Nakasho, Kazuhisa, Hiroyuki Okazaki, and Yasunari Shidama. "Finite Dimensional Real Normed Spaces are Proper Metric Spaces." Formalized Mathematics 29, no. 4 (December 1, 2021): 175–84. http://dx.doi.org/10.2478/forma-2021-0017.

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Summary In this article, we formalize in Mizar [1], [2] the topological properties of finite-dimensional real normed spaces. In the first section, we formalize the Bolzano-Weierstrass theorem, which states that a bounded sequence of points in an n-dimensional Euclidean space has a certain subsequence that converges to a point. As a corollary, it is also shown the equivalence between a subset of an n-dimensional Euclidean space being compact and being closed and bounded. In the next section, we formalize the definitions of L1-norm (Manhattan Norm) and maximum norm and show their topological equivalence in n-dimensional Euclidean spaces and finite-dimensional real linear spaces. In the last section, we formalize the linear isometries and their topological properties. Namely, it is shown that a linear isometry between real normed spaces preserves properties such as continuity, the convergence of a sequence, openness, closeness, and compactness of subsets. Finally, it is shown that finite-dimensional real normed spaces are proper metric spaces. We referred to [5], [9], and [7] in the formalization.

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40

BULAK, Fatma, and Hacer BOZKURT. "On Soft Normed Quasilinear Spaces." Journal of New Theory, no. 43 (June 30, 2023): 11–22. http://dx.doi.org/10.53570/jnt.1234191.

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In this study, we investigate some properties of soft quasi-sequences and present new results. We then study the completeness of soft normed quasilinear space and present an analog of convergence and boundness results of soft quasi sequences in soft normed quasilinear spaces. Moreover, we define regular and singular subspaces of soft quasilinear spaces and draw several conclusions related to these notions. Afterward, we provide examples of these results in soft normed quasilinear spaces generalizing well-known results in soft linear normed spaces. Additionally, we offer new results concerning soft quasi subspaces of soft normed quasilinear spaces. Finally, we discuss the need for further research.

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41

F. Al-Mayahi, Noori, and Abbas M. Abbas. "Some Properties of Spectral Theory in Fuzzy Hilbert Spaces." Journal of Al-Qadisiyah for computer science and mathematics 8, no. 2 (August 7, 2017): 1–7. http://dx.doi.org/10.29304/jqcm.2016.8.2.27.

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In this paper we give some definitions and properties of spectral theory in fuzzy Hilbert spaces also we introduce definitions Invariant under a linear operator on fuzzy normed spaces and reduced linear operator on fuzzy Hilbert spaces and we prove theorms related to eigenvalue and eigenvectors ,eigenspace in fuzzy normed , Invariant and reduced in fuzzy Hilbert spaces and show relationship between them.

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42

Jin, Zhen-Yu, and Cong-Hua Yan. "Fuzzifying bornological linear spaces." Journal of Intelligent & Fuzzy Systems 42, no. 3 (February 2, 2022): 2347–58. http://dx.doi.org/10.3233/jifs-211644.

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In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided.

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43

Peters, J. F. "Convex sets in proximal relator spaces." Filomat 30, no. 13 (2016): 3411–14. http://dx.doi.org/10.2298/fil1613411p.

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This article introduces convex sets in finite-dimensional normed linear spaces equipped with a proximal relator. A proximal relator is a nonvoid family of proximity relations R? (called a proximal relator) on a nonempty set. A normed linear space endowed with R? is an extension of the Sz?z relator space. This leads to a basis for the study of the nearness of convex sets in proximal linear spaces.

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44

Hamhalter, Jan. "Completeness and modular cross-symmetry in normed linear spaces." Czechoslovak Mathematical Journal 42, no. 1 (1992): 1–5. http://dx.doi.org/10.21136/cmj.1992.128311.

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45

Bayaz, Daraby, Delzendeh Fataneh, and Rahimi Asghar. "Parseval's equality in fuzzy normed linear spaces." MATHEMATICA 63 (86), no. 1 (May 20, 2021): 47–57. http://dx.doi.org/10.24193/mathcluj.2021.1.05.

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We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces are wider than for the category of the frames in the classical Hilbert spaces.

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46

Wu, Yaoqiang. "On (fuzzy) pseudo-semi-normed linear spaces." AIMS Mathematics 7, no. 1 (2021): 467–77. http://dx.doi.org/10.3934/math.2022030.

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<abstract><p>In this paper, we introduce the notion of pseudo-semi-normed linear spaces, following the concept of pseudo-norm which was presented by Schaefer and Wolff, and illustrate their relationship. On the other hand, we introduce the concept of fuzzy pseudo-semi-norm, which is weaker than the notion of fuzzy pseudo-norm initiated by N$ \tilde{\rm{a}} $d$ \tilde{\rm{a}} $ban. Moreover, we give some examples which are according to the commonly used $ t $-norms. Finally, we establish norm structures of fuzzy pseudo-semi-normed spaces and provide (fuzzy) topological spaces induced by (fuzzy) pseudo-semi-norms, and prove that the (fuzzy) topological spaces are (fuzzy) Hausdorff.</p></abstract>

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47

Ammari, Salsabila, Muh Nur, and Naimah Aris. "Fixed Point Theorem on Contractive Mapping in Standard 2-Normed Spaces." Jurnal Matematika, Statistika dan Komputasi 18, no. 1 (September 2, 2021): 93–101. http://dx.doi.org/10.20956/j.v18i1.14394.

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This paper discussed about the proof of the fixed point theorem on the standard 2-normed spaces by using completeness. The completeness of the standard 2-normed spaces is shown by defining a new norm. Two linear independent vectors on standard 2-normed spaces are used to define the new norm, namely which has been shown to be equivalent to standard norm.

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48

Bachir, A., and A. Segres. "Numerical range and orthogonality in normed spaces." Filomat 23, no. 1 (2009): 21–41. http://dx.doi.org/10.2298/fil0901021b.

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Introducing the concept of the normalized duality mapping on normed linear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkhoff-James orthogonality results in terms of the algebra numerical range V (T)A which generalize those given by J.P. William and J.P. Stamplfli. Finally, we give a positive answer of the Mathieu's question. .

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49

Strobin, Filip. "Porosity of Convex Nowhere Dense Subsets of Normed Linear Spaces." Abstract and Applied Analysis 2009 (2009): 1–11. http://dx.doi.org/10.1155/2009/243604.

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This paper is devoted to the following question: how to characterize convex nowhere dense subsets of normed linear spaces in terms of porosity? The motivation for this study originates from papers of V. Olevskii and L. Zajíček, where it is shown that convex nowhere dense subsets of normed linear spaces are porous in some strong senses.

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50

Gupta, Sahil, and T. D. Narang. "On strong proximinality in normed linear spaces." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 70, no. 1 (July 4, 2016): 19. http://dx.doi.org/10.17951/a.2016.70.1.19.

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The paper deals with strong proximinality in normed linear spaces. It is proved that in a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed.

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