scholarly journals On the Hyers-Ulam-Rassias stability problem for approximately k-additive mappings and functional inequalities

2007 ◽  
pp. 895-908
Author(s):  
Kil-Woung Jun ◽  
Hark-Mahn Kim
Keyword(s):  
Stability Problem ◽  
Functional Inequalities ◽  
Additive Mappings ◽  
Rassias Stability

scholarly journals Hyers–Ulam–Rassias Stability of Additive Mappings in Fuzzy Normed Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Jianrong Wu ◽  
Lingxiao Lu
Keyword(s):  
Functional Equations ◽  
Normed Spaces ◽  
Additive Mappings ◽  
Rassias Stability

In this paper, the Hyers–Ulam–Rassias stabilities of two functional equations, f a x + b y = r f x + s f y and f x + y + z = 2 f x + y / 2 + f z , are investigated in the framework of fuzzy normed spaces.

scholarly journals Functional Inequalities Associated with Additive Mappings

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Jaiok Roh ◽  
Ick-Soon Chang
Keyword(s):  
Banach Space ◽  
Functional Inequality ◽  
Functional Inequalities ◽  
Stability Theorems ◽  
Group Divisible ◽  
Additive Mappings

The functional inequality‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ  (x,y,z) (x,y,z∈G)is investigated, whereGis a group divisible by2,f:G→Xandϕ:G3→[0,∞)are mappings, andXis a Banach space. The main result of the paper states that the assumptions above together with (1)ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G)and (2)limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, orlimn→∞2nϕ(x/2n−1,y/2n,z/2n)=0  (x,y,z∈G), imply thatfis additive. In addition, some stability theorems are proved.

scholarly journals Stability of generalized additive Cauchy equations

2000 ◽  
Vol 24 (11) ◽  
pp. 721-727 ◽  
Author(s):  
Soon-Mo Jung ◽  
Ki-Suk Lee
Keyword(s):  
Functional Equation ◽  
Stability Problem ◽  
Cauchy Equation ◽  
Class Of Functions ◽  
Rassias Stability

A familiar functional equationf(ax+b)=cf(x)will be solved in the class of functionsf:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equationf(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1+⋯+aimxm)in connection with the question of Rassias and Tabor.

scholarly journals Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Young-Sun Cho ◽  
Hark-Mahn Kim
Keyword(s):  
Additive Mapping ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Additive Mappings

We investigate the generalized Hyers-Ulam stability of the functional inequalities associated with Cauchy-Jensen additive mappings. As a result, we obtain that if a mapping satisfies the functional inequalities with perturbation which satisfies certain conditions, then there exists a Cauchy-Jensen additive mapping near the mapping.

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