scholarly journals Stability of Cubic-Quartic Functional Equation in Multi-Fuzzy Banach Spaces

2018 ◽  
Vol 2 (1) ◽  
pp. 80-88
Author(s):  
Murali R ◽  
Antony Raj A
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Quartic Functional Equation ◽  
The Stability

In this paper we estabilish the Stability of Cubic-Quartic Functional Equations in Multi-Fuzzy Banach Spaces. g(2a + b) + g(2a − b) = 3g(a + b) + g(−a − b) + 3g(a − b) +g(b − a) + 18g(a) + 6g(−a) − 3g(b) − 3g(−b)

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

scholarly journals On the stability of radical septic functional equations

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2229
Author(s):  
Emanuel Guariglia ◽  
Kandhasamy Tamilvanan
Keyword(s):  
Functional Equation ◽  
Approximate Solution ◽  
Vector Space ◽  
Banach Spaces ◽  
Functional Equations ◽  
Normed Vector Space ◽  
Relevant Case ◽  
The Stability ◽  
Normed Vector ◽  
Stability Results

This paper deals with the approximate solution of the following functional equation fx7+y77=f(x)+f(y), where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach spaces and (β,p)-Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case.

scholarly journals On the Stability of Quadratic Functional Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Jung Rye Lee ◽  
Jong Su An ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
Banach Spaces ◽  
Functional Equations ◽  
Vector Spaces ◽  
Quadratic Functional ◽  
The Stability ◽  
Fixed Positive Integer ◽  
Rassias Stability

LetX,Ybe vector spaces andka fixed positive integer. It is shown that a mappingf(kx+y)+f(kx-y)=2k2f(x)+2f(y)for allx,y∈Xif and only if the mappingf:X→Ysatisfiesf(x+y)+f(x-y)=2f(x)+2f(y)for allx,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.

scholarly journals On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach 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.

scholarly journals The Stability Analysis of A-Quartic Functional Equation

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2881
Author(s):  
Chinnaappu Muthamilarasi ◽  
Shyam Sundar Santra ◽  
Ganapathy Balasubramanian ◽  
Vediyappan Govindan ◽  
Rami Ahmad El-Nabulsi ◽  
...  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Stability Analysis ◽  
General Solution ◽  
Banach Spaces ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
Fixed Point Methods ◽  
The Stability

In this paper, we study the general solution of the functional equation, which is derived from additive–quartic mappings. In addition, we establish the generalized Hyers–Ulam stability of the additive–quartic functional equation in Banach spaces by using direct and fixed point methods.

scholarly journals Ulam Stability of a Functional Equation in Various Normed Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1119
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Direct Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quadratic Mappings ◽  
The Stability

In this note, we study the Ulam stability of a general functional equation in four variables. Since its particular case is a known equation characterizing the so-called bi-quadratic mappings (i.e., mappings which are quadratic in each of their both arguments), we get in consequence its stability, too. We deal with the stability of the considered functional equations not only in classical Banach spaces, but also in 2-Banach and complete non-Archimedean normed spaces. To obtain our outcomes, the direct method is applied.

scholarly journals A Remark for the Hyers–Ulam Stabilities on n-Banach Spaces

Axioms ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Jaeyoo Choy ◽  
Hahng-Yun Chu ◽  
Ahyoung Kim
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Cubic Functional Equation ◽  
Quartic Functional Equation ◽  
Surjective Mapping

In this article, we deal with stabilities of several functional equations in n-Banach spaces. For a surjective mapping f into a n-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic functional equation for f in n-Banach spaces.

scholarly journals Stability of an Additive-Cubic-Quartic Functional Equation in Multi-Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Zhihua Wang ◽  
Xiaopei Li ◽  
Themistocles M. Rassias
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Ulam Stability ◽  
Alternative Method ◽  
Quartic Functional Equation ◽  
First Results ◽  
The Stability

We prove the Hyers-Ulam stability of the additive-cubic-quartic functional equation in multi-Banach spaces by using the fixed point alternative method. The first results on the stability in the multi-Banach spaces were presented in (Dales and Moslehian 2007).

scholarly journals Fuzzy Stability Results of Generalized Quartic Functional Equations

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 120
Author(s):  
Sang Og Kim ◽  
Kandhasamy Tamilvanan
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Control Function ◽  
Direct Method ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
New Type ◽  
The Stability ◽  
Fixed Point Techniques ◽  
Stability Results

In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable.

Sign in / Sign up

Export Citation Format

Share Document