On functional equations of homological type for generalized functions on ?n

1993 ◽  
Vol 54 (6) ◽  
pp. 1291-1292
Author(s):  
E. V. Shul'man
Keyword(s):  
Functional Equations ◽  
Generalized Functions ◽  
Homological Type

scholarly journals On the Stability of Trigonometric Functional Equations in Distributions and Hyperfunctions

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jaeyoung Chung ◽  
Jeongwook Chang
Keyword(s):  
Functional Equations ◽  
Generalized Functions ◽  
Ulam Stability ◽  
Schwartz Distributions ◽  
The Stability

We consider the Hyers-Ulam stability for a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand hyperfunctions.

Some functional equations in the spaces of generalized functions

2003 ◽  
Vol 65 (3) ◽  
pp. 267-279 ◽  
Author(s):  
Jaeyoung Chung ◽  
Shinyoung Lee
Keyword(s):  
Functional Equations ◽  
Generalized Functions

scholarly journals Linear algebra and differential geometry on abstract Hilbert space

2005 ◽  
Vol 2005 (14) ◽  
pp. 2241-2275 ◽  
Author(s):  
Alexey A. Kryukov
Keyword(s):  
Differential Geometry ◽  
Hilbert Space ◽  
Linear Algebra ◽  
Hilbert Spaces ◽  
Functional Equations ◽  
Generalized Functions ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Simple Observation ◽  
Local Coordinates

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms ofn-dimensional vector spaces. However, whilen-dimensional spaces in applications are always realized as the Euclidean spaceRn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. Images of charts on manifolds in the formalism are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations then describe families of functional equations on various spaces of functions. The formalism itself and its applications in linear algebra, differential equations, and differential geometry are carefully analyzed.

On some functional equations related to derivations and bicircular projections in rings

2014 ◽  
Vol 49 (2) ◽  
pp. 313-331
Author(s):  
Maja Fošner ◽  
◽  
Benjamin Marcen ◽  
Nejc Širovnik ◽  
Joso Vukman ◽  
...  
Keyword(s):  
Functional Equations

Functional equations related to weightable quasi-metrics

2015 ◽  
Vol 4 (1047) ◽  
Author(s):  
M.J. Campion ◽  
E. Indurain ◽  
G. Ochoa
Keyword(s):  
Functional Equations

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.

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