scholarly journals RN HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS: A DIRECT METHOD

2014 ◽  
Vol 95 (1) ◽  
Author(s):  
D.Y. Shin ◽  
H.A. Kenary ◽  
N. Sahami
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
Stability Of Functional Equations ◽  
A Direct Method ◽  
Rassias Stability

scholarly journals Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy Banach spaces.

scholarly journals Direct Method and Approximation of the Reciprocal Difference Functional Equations in Various Normed Spaces

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
H. Azadi Kenary
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
Normed Spaces ◽  
Reciprocal Difference ◽  
Rassias Stability

AbstractIn this paper, using direct method, we prove the generalized Hyers- Ulam-Rassias stability of the reciprocal difference functional equations in various normed spaces.

scholarly journals On new stability results for composite functional equations in quasi-β-normed spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 68-84
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Functional Equations ◽  
Direct Method ◽  
Functional Inequality ◽  
Fixed Point Method ◽  
Normed Spaces ◽  
Composite Functional Equations ◽  
Stability Results ◽  
Rassias Stability

Abstract In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f ( f ( x ) − f ( y ) ) = f ( x + y ) + f ( x − y ) − f ( x ) − f ( y ) , f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where f f maps from a ( β , p ) \left(\beta ,p) -Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s s -functional inequality is discussed via our results.

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