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.

scholarly journals A Gauss type functional equation

2001 ◽  
Vol 25 (9) ◽  
pp. 565-569 ◽  
Author(s):  
Silvia Toader ◽  
Themistocles M. Rassias ◽  
Gheorghe Toader
Keyword(s):  
Functional Equation ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Gauss Type

Gauss' functional equation (used in the study of the arithmetic-geometric mean) is generalized by replacing the arithmetic mean and the geometric mean by two arbitrary means.

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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