Ulam-Hyers Stability of Functional Equations in Quasi-β-Banach Spaces

2019 ◽  
pp. 97-130
Author(s):  
Nguyen Van Dung ◽  
Wutiphol Sintunavarat
Keyword(s):  
Banach Spaces ◽  
Functional Equations ◽  
Stability Of Functional Equations

scholarly journals Ulam stability of functional equations in 2-Banach spaces via the fixed point method

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Several Variables ◽  
Stability Of Functional Equations ◽  
Special Cases ◽  
The Stability

AbstractUsing the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

A fixed point approach to the hyperstability of the general linear equation in β-Banach spaces

Analysis ◽  
2018 ◽  
Vol 38 (3) ◽  
pp. 115-126
Author(s):  
Iz-iddine EL-Fassi ◽  
Samir Kabbaj ◽  
Abdellatif Chahbi
Keyword(s):  
Fixed Point ◽  
Linear Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
General Linear ◽  
General Linear Equation ◽  
Fixed Point Approach ◽  
Nonlinear Anal ◽  
Stability Of Functional Equations ◽  
The Fixed Point Theorem

AbstractThe purpose of this paper is first to reformulate the fixed point theorem (see Theorem 1 of [J. Brzdȩk, J. Chudziak and Z. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 2011, 17, 6728–6732]) in β-Banach spaces. We also show that this theorem is a very efficient and convenient tool for proving the hyperstability results of the general linear equation in β-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it.

scholarly journals Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

scholarly journals Additive ρ-functional inequalities in β-homogeneous normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1651-1658
Author(s):  
Choonkil Park
Keyword(s):  
Banach Spaces ◽  
Complex Number ◽  
Functional Equations ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Homogeneous Complex ◽  
Fixed Complex

In this paper, we solve the following additive ?-functional inequalities ||f (x + y) - f (x) - f (y)|| ? ???(2f (x+y/2) - f(x) + -f (y))??, (1) where ? is a fixed complex number with |?|<1, and ??2f(x+y/2)-f(x)- f(y)???||?(f(x+y)-f(x)-f(y))||, (2) where ? is a fixed complex number with |?|<1/2 , and prove the Hyers-Ulam stability of the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive ?-functional equations associated with the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces.

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