On some nonlinear volterra integral-functional equation in several variables

1994 ◽  
Vol 20 (4) ◽  
pp. 241-253 ◽  
Author(s):  
Tomasz Człapiński
Keyword(s):  
Functional Equation ◽  
Integral Functional ◽  
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.

scholarly journals On a Certain Generalized Functional Equation for Set-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2243
Author(s):  
Yaroslav Bazaykin ◽  
Dušan Bednařík ◽  
Veronika Borůvková ◽  
Tomáš Zuščák
Keyword(s):  
Functional Equation ◽  
Integral Functional ◽  
Asplund Space ◽  
Invariant Metric ◽  
Real Vector ◽  
Linear Metric Space ◽  
Real Linear ◽  
The Right ◽  
Locally Convex ◽  
Generalized Type

The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function F:X→cc(Y), where X is a real vector space and Y is a locally convex real linear metric space with an invariant metric. Most general results are described in the case of a compact topological group G equipped with the right-invariant Haar measure acting on X. Further results are found if the group G is finite or Y is Asplund space. The main results are applied to an example where X=R2 and Y=Rn, n∈N, and G is the unitary group U(1).

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