scholarly journals Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Zolfaghari ◽  
J. M. Rassias ◽  
M. B. Savadkouhi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quartic Functional Equation

We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equationf(x+2y)+f(x−2y)=4(f(x+y)+f(x−y))−24f(y)−6f(x)+3f(2y)in quasi-Banach spaces.

scholarly journals Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
Hark-Mahn Kim
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
Linear Spaces ◽  
Quadratic Mappings

we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability inp-Banach spaces.

scholarly journals Approximation of Mixed Euler-Lagrange σ -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
John Michael Rassias ◽  
Narasimman Pasupathi ◽  
Reza Saadati ◽  
Manuel de la Sen
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Linear Space ◽  
Mixed Type ◽  
Normed Linear Space ◽  
Research Paper ◽  
Quartic Functional Equation

In this research paper, the authors present a new mixed Euler-Lagrange σ -cubic-quartic functional equation. For this introduced mixed type functional equation, the authors obtain general solution and investigate the various stabilities related to the Ulam problem in Felbin’s type of fuzzy normed linear space (f-NLS) with suitable counterexamples. This approach leads us to approximate the Euler-Lagrange σ -cubic-quartic functional equation with better estimation.

scholarly journals Stability of a Quartic Functional Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
Fixed Positive Integer

We obtain the general solution of the generalized quartic functional equationf(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y)+f(x-y)}for a fixed positive integerm. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean 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 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.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

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 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.

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