Generalizations Of A “folk-Theorem” On Simple Functional Equations In A Single Variable

1991 ◽  
Vol 19 (1-2) ◽  
pp. 5-21 ◽  
Author(s):  
János Aczél ◽  
Marek Kuczma
Keyword(s):  
Functional Equations ◽  
Folk Theorem ◽  
Single Variable

scholarly journals Stability of functional equations in single variable

2003 ◽  
Vol 288 (2) ◽  
pp. 852-869 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Bing Xu ◽  
Weinian Zhang
Keyword(s):  
Functional Equations ◽  
Single Variable ◽  
Stability Of Functional Equations

scholarly journals Fixed Points and Generalized Hyers-Ulam Stability

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
L. Cădariu ◽  
L. Găvruţa ◽  
P. Găvruţa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Open Problem ◽  
Functional Equations ◽  
Affirmative Answer ◽  
Ulam Stability ◽  
Single Variable ◽  
Result Show

In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdęk et al., (2011) and Brzdęk and Ciepliński (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdęk and Ciepliński (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable.

On a class of composite functional equations in a single variable

1996 ◽  
Vol 52 (1) ◽  
pp. 260-283 ◽  
Author(s):  
P. Kahlig ◽  
A. Matkowska ◽  
J. Matkowski
Keyword(s):  
Functional Equations ◽  
Single Variable ◽  
Composite Functional Equations

scholarly journals Inclusions in a Single Variable in Ultrametric Spaces and Hyers-Ulam Stability

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Magdalena Piszczek
Keyword(s):  
Functional Equations ◽  
Ulam Stability ◽  
Single Variable ◽  
Ultrametric Spaces ◽  
Stability Results

We present some properties of set-valued inclusions in a single variable in ultrametric spaces. As a consequence, we obtain stability results for the corresponding functional equations.

On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Magdalena Piszczek
Keyword(s):  
Functional Equations ◽  
Linear Equations ◽  
Single Variable ◽  
The Stability

AbstractWe present the results on the stability of some set-valued functional equations with applications to the gamma-type equations or linear equations.

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