scholarly journals On the Hyers–Ulam–Rassias stability of generalized quadratic mappings in Banach modules

2004 ◽  
Vol 291 (1) ◽  
pp. 214-223 ◽  
Author(s):  
Chun-Gil Park
Keyword(s):  
Quadratic Mappings ◽  
Banach Modules ◽  
Rassias Stability

scholarly journals On the Generalized Ulam-Hyers-Rassias Stability of Quadratic Mappings in Modular Spaces withoutΔ2-Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Kittipong Wongkum ◽  
Parin Chaipunya ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Lower Semicontinuous ◽  
Point Theory ◽  
Quadratic Functional ◽  
Modular Spaces ◽  
Quadratic Mappings ◽  
Rassias Stability

We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives ofΔ2-conditions.

scholarly journals Stability of linear functional equations in Banach modules

2004 ◽  
Vol 35 (1) ◽  
pp. 29-36
Author(s):  
Chun-Gil Park
Keyword(s):  
Functional Equation ◽  
Banach Algebra ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Functional Equation ◽  
Linear Functional Equations ◽  
Banach Modules ◽  
Unital Banach Algebra ◽  
Rassias Stability

We prove the Hyers-Ulam-Rassias stability of the linear functional equation in Banach modules over a unital Banach algebra.

Fixed Points and Stability for Quadratic Mappings in β–Normed Left Banach Modules on Banach Algebras

2011 ◽  
Vol 61 (3-4) ◽  
pp. 393-400 ◽  
Author(s):  
M. Eshaghi. Gordji ◽  
H. Khodaei ◽  
Th. M. Rassias
Keyword(s):  
Fixed Points ◽  
Banach Algebras ◽  
Quadratic Mappings ◽  
Banach Modules

scholarly journals Hyers-Ulam-Rassias RNS Approximation of Euler-Lagrange-Type Additive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Azadi Kenary ◽  
H. Rezaei ◽  
A. Ebadian ◽  
A. R. Zohdi
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Banach Modules ◽  
Random Normed Spaces ◽  
Additive Mappings ◽  
Rassias Stability

Recently the generalized Hyers-Ulam (or Hyers-Ulam-Rassias) stability of the following functional equation∑j=1mf(-rjxj+∑1≤i≤m,i≠jrixi)+2∑i=1mrif(xi)=mf(∑i=1mrixi)wherer1,…,rm∈R, proved in Banach modules over a unitalC*-algebra. It was shown that if∑i=1mri≠0,ri,rj≠0for some1≤i<j≤mand a mappingf:X→Ysatisfies the above mentioned functional equation then the mappingf:X→Yis Cauchy additive. In this paper we prove the Hyers-Ulam-Rassias stability of the above mentioned functional equation in random normed spaces (briefly RNS).

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