scholarly journals Superstability of functional equations related to spherical functions

2017 ◽  
Vol 15 (1) ◽  
pp. 427-432 ◽  
Author(s):  
László Székelyhidi
Keyword(s):  
Functional Equations ◽  
Spherical Functions ◽  
Invariant Means ◽  
Stability Type

Abstract In this paper we prove stability-type theorems for functional equations related to spherical functions. Our proofs are based on superstability-type methods and on the method of invariant means.

Functional equations and matrix-valued spherical functions

2005 ◽  
Vol 69 (3) ◽  
pp. 271-292 ◽  
Author(s):  
Henrik Stetkær
Keyword(s):  
Functional Equations ◽  
Spherical Functions

scholarly journals Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations

2005 ◽  
Vol 12 (2) ◽  
pp. 207-216
Author(s):  
Belaid Bouikhalene ◽  
Samir Kabbaj
Keyword(s):  
Functional Equations ◽  
Spherical Functions ◽  
Aequationes Math ◽  
Gelfand Pairs

Abstract We show that Cauchy's, d'Alembert's functional equations and their generalizations are the functional equations for bounded spherical functions associated to some Gel'fand pairs. Our results are very close to the ones obtained by Stetkær in [Aequationes Math. 48: 220–227, 1994].

scholarly journals Invariant Means, Complementary Averages of Means, and a Characterization of the Beta-Type Means

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1753
Author(s):  
Janusz Matkowski ◽  
Paweł Pasteczka
Keyword(s):  
Functional Equations ◽  
Nonempty Subset ◽  
Invariant Mean ◽  
Type Mapping ◽  
The Mean ◽  
Invariant Means

We prove that whenever the selfmapping (M1,…,Mp):Ip→Ip, (p∈N and Mi-s are p-variable means on the interval I) is invariant with respect to some continuous and strictly monotone mean K:Ip→I then for every nonempty subset S⊆{1,…,p} there exists a uniquely determined mean KS:Ip→I such that the mean-type mapping (N1,…,Np):Ip→Ip is K-invariant, where Ni:=KS for i∈S and Ni:=Mi otherwise. Moreover min(Mi:i∈S)≤KS≤max(Mi:i∈S). Later we use this result to: (1) construct a broad family of K-invariant mean-type mappings, (2) solve functional equations of invariant-type, and (3) characterize Beta-type means.

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

Harmonic Analysis of Spherical Functions on Real Reductive Groups

1988 ◽  
Author(s):  
Ramesh Gangolli ◽  
Veeravalli S. Varadarajan
Keyword(s):  
Harmonic Analysis ◽  
Spherical Functions ◽  
Reductive Groups

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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