Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/weak-n-inner-product-spaces-0zVudP5dsu
References (32)
-
H. Gunawan (2018)
n-Inner Products, n-Norms, and Angles Between Two Subspaces -
K. Raj, S. Jamwal (2016)
Applications of statistical convergence to n-normed spacesAdvances in Pure and Applied Mathematics, 7
-
S. Gudder (1974)
Inner Product SpacesAmerican Mathematical Monthly, 81
-
(2018)
Lacunary I-convergent and lacunary I-bounded sequence spaces defined by a Musielak–Orlicz function over n-normed spaces -
Cezar Lupu, D. Schwarz (2014)
Another look at some new Cauchy-Schwarz type inner product inequalitiesAppl. Math. Comput., 231
-
Grey Giddins (2016)
StatisticsJournal of Hand Surgery (European Volume), 41
-
K. Raj (2018)
SOME GENERALIZED SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTIONS IN N-NORMED SPACES -
Charles Diminnie (1973)
2-inner product spaces, 6
-
S. Dragomir, Y. Cho, S. Kim, A. Sofo (2003)
Some Boas-Bellman Type Inequalities in 2-Inner Product SpacesMathematics eJournal
-
A. Misiak (1989)
n-Inner Product Spaces†Mathematische Nachrichten, 140
-
C. Dodgson (2014)
An Elementary Treatise on Determinants: With Their Application to Simultaneous Linear Equations and Algebraical Geometry -
Rev. Dodgson
IV. Condensation of determinants, being a new and brief method for computing their arithmetical valuesProceedings of the Royal Society of London
-
Charles Diminnie, S. Gâhler, A. White (1977)
2-INNER PRODUCT SPACES II1)Demonstratio Mathematica, 10
-
L. Carroll, F. Abeles (1994)
The mathematical pamphlets of Charles Lutwidge Dodgson and related pieces -
M. Niezgoda (2007)
On the Chebyshev functionalMathematical Inequalities & Applications
-
H. Gunawan (2003)
INNER PRODUCTS ON n-INNER PRODUCT SPACES -
Y. Cho, M. Matic, J. Pečarić (2004)
ON GRAM'S DETERMINANT IN n-INNER PRODUCT SPACESBulletin of The Korean Mathematical Society, 41
-
Pabitra Debnath, M. Saha (2018)
Categorization of n-inner Product SpaceAsian Research Journal of Mathematics
-
G. Gehér (2015)
On $$\varvec{n}$$n-norm preservers and the Aleksandrov conservative $$\varvec{n}$$n-distance problemAequationes mathematicae, 91
-
Nazneen Khan (2016)
Classes of -Convergent Double Sequences over -Normed SpacesJournal of Function Spaces and Applications, 2016
-
Xujian Huang, D. Tan (2019)
A Tingley’s type problem in n-normed spacesAequationes mathematicae
-
S. Gähler (1964)
Lineare 2-normierte Räume†Mathematische Nachrichten, 28
-
G. Gehér (2017)
On n -norm preservers and the Aleksandrov conservative n -distance problem -
Y. Cho, M. Matic, J. Pečarić (2001)
ON GRAMS DETERMINANT IN 2-INNER PRODUCT SPACESJournal of The Korean Mathematical Society, 38
-
Nazneen Khan (2016)
Classes of I-Convergent Double Sequences over n-Normed Spaces -
Charles Diminnie (1977)
2-inner product spaces. II, 10
-
J. Brzdȩk, K. Ciepliński (2019)
A fixed point theorem in n-Banach spaces and Ulam stabilityJournal of Mathematical Analysis and Applications
-
S. Mohiuddine, S. Sharma, Dina Abuzaid (2018)
Some Seminormed Difference Sequence Spaces over -Normed Spaces Defined by a Musielak-Orlicz Function of OrderJournal of Function Spaces and Applications, 2018
-
James Evans (1999)
Statistics, Data Analysis, and Decision Modeling -
A. Misiak (1989)
Orthogonality and Orthonormality in n‐Inner Product SpacesMathematische Nachrichten, 143
-
F. Abeles (2014)
Chiò's and Dodgson's determinantal identitiesLinear Algebra and its Applications, 454
-
H. Eves (1980)
Elementary Matrix Theory
- Publisher
- Springer Journals
- Copyright
- Copyright © Tusi Mathematical Research Group (TMRG) 2021
- ISSN
- 2639-7390
- eISSN
- 2008-8752
- DOI
- 10.1007/s43034-020-00108-3
- Publisher site
- See Article on Publisher Site
Abstract
In this article, we study a generalization of the n-inner product which we name weak n-inner product. As particular case, we consider the n-iterated 2-inner product and we give its representation in terms of the standard k-inner products, k≤n\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k\le n$$\end{document}, using the Dodgson’s identity for determinants. Finally, we present several applications, including a brief characterization of a linear regression model for the random variables in discrete case and a generalization of the Chebyshev functional using the n-iterated 2-inner product.
Journal
Annals of Functional Analysis – Springer Journals
Published: Jan 26, 2021