Non-archimedean stability and non-stability of quadratic reciprocal functional equation in several variables

2018 ◽  
Vol 37e (2) ◽  
pp. 267
Author(s):  
Nawneet Hooda ◽  
Shalini Tomar
Keyword(s):  
Functional Equation ◽  
Several Variables

scholarly journals On the Beckenbach–Gini–Lehmer Means and Means Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1569
Author(s):  
Janusz Matkowski ◽  
Małgorzata Wróbel
Keyword(s):  
Functional Equation ◽  
Arithmetic Mean ◽  
Several Variables ◽  
Equality Of Means

Beckenbacg–Gini–Lehmer type means and mean-type mappings generated by functions of several variables, for which the arithmetic mean is invariant, are introduced. Equality of means of that type, their homogeneity, and convergence of the iterates of the respective mean-type mappings are considered. An application to solving a functional equation is given.

ON HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2015 ◽  
Vol 92 (2) ◽  
pp. 259-267 ◽  
Author(s):  
DONG ZHANG
Keyword(s):  
Functional Equation ◽  
Exact Solutions ◽  
Normed Space ◽  
Functional Equations ◽  
Linear Functional ◽  
Approximate Solutions ◽  
Linear Functional Equation ◽  
Several Variables ◽  
Linear Functional Equations

We obtain some results on approximate solutions of the generalised linear functional equation $\sum _{i=1}^{m}L_{i}f(\sum _{j=1}^{n}a_{ij}x_{j})=0$ for functions mapping a normed space into a normed space. We show that, under suitable assumptions, the approximate solutions are in fact exact solutions. The theorems correspond to and complement recent results on the hyperstability of generalised linear functional equations.

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