scholarly journals A survey on the stability of mean value points and functional equations involving some special functions

2015 ◽  
Vol 24 (1) ◽  
pp. 27-42
Author(s):  
SORINEL DUMITRESCU ◽  
◽  
MIHAI MONEA ◽  
CRISTINEL MORTICI ◽  
◽  
...  
Keyword(s):  
Functional Equations ◽  
Special Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
The Stability

The aim of this work is to put together some of the recent and classical results in the theory of stability. In the first part, we recall the results regarding the intermediary points arising from various Mean Value Theorems, then we study the stability of some functional equations involving the gamma and beta functions.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

Mean Value Theorems and Linear Operators

1955 ◽  
Vol 62 (4) ◽  
pp. 217 ◽  
Author(s):  
Philip Hartman ◽  
Aurel Wintner
Keyword(s):  
Mean Value ◽  
Linear Operators ◽  
Mean Value Theorems

scholarly journals Some remarks on the stability of the Cauchy equation and completeness

2021 ◽  
Author(s):  
Harald Fripertinger ◽  
Jens Schwaiger
Keyword(s):  
Normed Space ◽  
Additive Function ◽  
Functional Equations ◽  
Constant Function ◽  
Cauchy Equation ◽  
Cauchy Difference ◽  
International Conference ◽  
The Difference ◽  
The Stability ◽  
The Given

AbstractIt was proved in Forti and Schwaiger (C R Math Acad Sci Soc R Can 11(6):215–220, 1989), Schwaiger (Aequ Math 35:120–121, 1988) and with different methods in Schwaiger (Developments in functional equations and related topics. Selected papers based on the presentations at the 16th international conference on functional equations and inequalities, ICFEI, Bȩdlewo, Poland, May 17–23, 2015, Springer, Cham, pp 275–295, 2017) that under the assumption that every function defined on suitable abelian semigroups with values in a normed space such that the norm of its Cauchy difference is bounded by a constant (function) is close to some additive function, i.e., the norm of the difference between the given function and that additive function is also bounded by a constant, the normed space must necessarily be complete. By Schwaiger (Ann Math Sil 34:151–163, 2020) this is also true in the non-archimedean case. Here we discuss the situation when the bound is a suitable non-constant function.

scholarly journals On the stability of set-valued functional equations with the fixed point alternative

2012 ◽  
Vol 2012 (1) ◽  
pp. 81 ◽  
Author(s):  
Hassan Kenary ◽  
Hamid Rezaei ◽  
Yousof Gheisari ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
The Stability

scholarly journals A family of the Cauchy type mean-value theorems

2005 ◽  
Vol 306 (2) ◽  
pp. 730-739 ◽  
Author(s):  
Josip E. Pečarić ◽  
Ivan Perić ◽  
H.M. Srivastava
Keyword(s):  
Mean Value ◽  
Cauchy Type ◽  
Mean Value Theorems
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