scholarly journals Orthogonal Stability and Nonstability of a Generalized Quartic Functional Equation in Quasi- β -Normed Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Nazek Alessa ◽  
K. Tamilvanan ◽  
K. Loganathan ◽  
T. S. Karthik ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Quartic Functional Equation

In this work, we examine the generalized Hyers-Ulam orthogonal stability of the quartic functional equation in quasi- β -normed spaces. Moreover, we prove that this functional equation is not stable in a special condition by a counterexample.

scholarly journals Approximate mixed type additive and quartic functional equation

2017 ◽  
Vol 35 (1) ◽  
pp. 43 ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Mixed Type ◽  
Current Work ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
All Solutions

In the current work, we introduce a general form of a mixed additive and quartic functional equation. We determine all solutions of this functional equation. We also establish the generalized Hyers-Ulam stability of this new functional equation in quasi-$\beta$-normed spaces.

scholarly journals Nonlinear Random Stability via Fixed-Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-45 ◽  
Author(s):  
Yeol Je Cho ◽  
Shin Min Kang ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
Random Normed Spaces

We prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in various complete random normed spaces.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

Solution of the Ulam stability problem for Euler–Lagrange k-quintic mappings

2020 ◽  
Vol 27 (4) ◽  
pp. 585-592
Author(s):  
Syed Abdul Mohiuddine ◽  
John Michael Rassias ◽  
Abdullah Alotaibi
Keyword(s):  
Functional Equation ◽  
Stability Problem ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Stability Problems ◽  
Quartic Functional Equation ◽  
Ulam Stability Problem

AbstractThe “oldest quartic” functional equationf(x+2y)+f(x-2y)=4[f(x+y)+f(x-y)]-6f(x)+24f(y)was introduced and solved by the second author of this paper (see J. M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. III 34(54) 1999, 2, 243–252). Similarly, an interesting “quintic” functional equation was introduced and investigated by I. G. Cho, D. Kang and H. Koh, Stability problems of quintic mappings in quasi-β-normed spaces, J. Inequal. Appl. 2010 2010, Article ID 368981, in the following form:2f(2x+y)+2f(2x-y)+f(x+2y)+f(x-2y)=20[f(x+y)+f(x-y)]+90f(x).In this paper, we generalize this “Cho–Kang–Koh equation” by introducing pertinent Euler–Lagrange k-quintic functional equations, and investigate the “Ulam stability” of these new k-quintic functional mappings.

scholarly journals Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 130-146
Author(s):  
Yachai Liu ◽  
Xiuzhong Yang ◽  
Guofen Liu
Keyword(s):  
Functional Equation ◽  
Direct Method ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
Rassias Stability

AbstractIn this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$in non-Archimedean (n, β)-normed spaces.

scholarly journals Stability of a mixed type additive and quartic functional equation

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1629-1640 ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Mixed Type ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
Random Normed Spaces

In this paper we obtain the general solution of a mixed additive and quartic functional equation. We also prove the Hyers-Ulam stability of this functional equation in random normed spaces.

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