Symmetrized Birkhoff–James orthogonality in arbitrary normed spaces

2021 ◽  
pp. 125203
Author(s):  
Ljiljana Arambašić ◽  
Alexander Guterman ◽  
Bojan Kuzma ◽  
Rajna Rajić ◽  
Svetlana Zhilina
Keyword(s):  
Normed Spaces ◽  
James Orthogonality

scholarly journals Numerical range and orthogonality in normed spaces

Filomat ◽  
2009 ◽  
Vol 23 (1) ◽  
pp. 21-41 ◽  
Author(s):  
A. Bachir ◽  
A. Segres
Keyword(s):  
Normed Linear Space ◽  
Numerical Range ◽  
Positive Answer ◽  
Duality Mapping ◽  
Normed Algebra ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normalized Duality Mapping ◽  
James Orthogonality ◽  
Orthogonality In Normed Spaces

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. .

2-HH NORM AND BIRKHOFF-JAMES ORTHOGONALITY IN NORMED SPACES

2019 ◽  
Vol 8 (3) ◽  
pp. 1
Author(s):  
PRASAD OJHA BHUWAN ◽  
MUNI BAJRACHARYA PRAKASH ◽  
◽  
Keyword(s):  
Normed Spaces ◽  
James Orthogonality ◽  
Orthogonality In Normed Spaces

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

scholarly journals Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

Operators preserving mutual strong Birkhoff–James orthogonality on B(H)

2021 ◽  
Author(s):  
Ljiljana Arambašić ◽  
Alexander Guterman ◽  
Bojan Kuzma ◽  
Rajna Rajić ◽  
Svetlana Zhilina
Keyword(s):  
James Orthogonality

Strong and pure fixed point properties of mappings on normed spaces

2021 ◽  
Author(s):  
Hüseyin Işık ◽  
Vahid Parvaneh ◽  
Mohammad Reza Haddadi
Keyword(s):  
Fixed Point ◽  
Normed Spaces ◽  
Fixed Point Properties
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