Series Expansions for the Solution of an Integral-Functional Equation with a Parameter

2002 ◽  
Vol 41 (3-4) ◽  
pp. 213-228 ◽  
Author(s):  
L. Berg ◽  
M. Krüppel
Keyword(s):  
Functional Equation ◽  
Integral Functional ◽  
Series Expansions

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).

On The Solvability of Nonlinear Integral Functional Equation

2016 ◽  
Vol 34 (1) ◽  
pp. 39-44
Author(s):  
Mahmoud M. El-Borai ◽  
◽  
Wagdy G. El-Sayed ◽  
Faez N. Ghaffoori
Keyword(s):  
Functional Equation ◽  
Integral Functional
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