scholarly journals Recent results on functional equations in a single variable, perspectives and open problems

2001 ◽  
Vol 61 (1-2) ◽  
pp. 1-48 ◽  
Author(s):  
K. Baron
Keyword(s):  
Functional Equations ◽  
Single Variable ◽  
Open Problems

Iteration Theory: Dynamical Systems and Functional Equations

2003 ◽  
Vol 13 (07) ◽  
pp. 1627-1647 ◽  
Author(s):  
F. Balibrea ◽  
L. Reich ◽  
J. Smítal
Keyword(s):  
Dynamical Systems ◽  
Functional Equations ◽  
Discrete Dynamical Systems ◽  
Iteration Theory ◽  
Open Problems ◽  
Research Directions ◽  
The Past ◽  
New Research

The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.

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

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 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.

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