scholarly journals Stability of Cubic Functional Equation in Random Normed Space

2018 ◽  
Vol 14 (2) ◽  
pp. 7864-7877 ◽  
Author(s):  
Sandra Pinelas ◽  
V. Govindan ◽  
K. Tamilvanan
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Ulam Stability ◽  
Cubic Functional Equation ◽  
Random Normed Space

In this paper, we present the Hyers-Ulam stability of Cubic functional equation. where n is greater than or equal to 4, in Random Normed Space.

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.

GENERALIZED HYERS-ULAM STABILITY FOR A GENERAL CUBIC FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES

2011 ◽  
Vol 04 (03) ◽  
pp. 413-425 ◽  
Author(s):  
G. Z. Eskandani ◽  
J. M. Rassias ◽  
P. Gavruta
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation

In this paper, we investigate the generalized Hyers-Ulam stability of the following general cubic functional equation [Formula: see text] (k ∈ ℕ, k ≠ 1) in quasi-β-normed spaces and by a counterexample, we will show that this functional equation in a special condition is not stabile.

scholarly journals Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1050 ◽  
Author(s):  
Abdulaziz M. Alanazi ◽  
G. Muhiuddin ◽  
K. Tamilvanan ◽  
Ebtehaj N. Alenze ◽  
Abdelhalim Ebaid ◽  
...  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Normed Space ◽  
Additive Functional ◽  
Current Work ◽  
Ulam Stability ◽  
Fuzzy Normed Space ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.

scholarly journals Approximate Cubic Lie Derivations on ρ-Complete Convex Modular Algebras

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Hark-Mahn Kim ◽  
Hwan-Yong Shin
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Cubic Functional Equation ◽  
Stability Results ◽  
Lie Derivations

In this article, we present generalized Hyers–Ulam stability results of a cubic functional equation associated with an approximate cubic Lie derivations on convex modular algebras χρ with Δ2-condition on the convex modular functional ρ.

scholarly journals On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation inn-Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Tian Zhou Xu ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Direct Method ◽  
Ulam Stability ◽  
Cubic Functional Equation ◽  
Cubic Function

The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation inn-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.

scholarly journals Nonlinear L-fuzzy stability of k-cubic functional equation

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1137-1148 ◽  
Author(s):  
Reza Saadati ◽  
Yeol Cho ◽  
John Rassias
Keyword(s):  
Functional Equation ◽  
Set Theory ◽  
Normed Space ◽  
Lattice Theory ◽  
Functional Equations ◽  
Stability Result ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Cubic Functional Equation ◽  
The Stability

In this paper, we establish the stability result for the k-cubic functional equation 2[kf (x+ky)+f (kx-y)]=k(k2+1)[f(x+y)+f(x-y)] + 2(k4-1) f(y), where k is a real number different from 0 and 1, in the setting of various L-fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First we shall prove the stability of k-cubic functional equations in the L-fuzzy normed space under arbitrary t-norm which generalizes previous works. Then we prove the stability of k-cubic functional equations in the non- Archimedean L-fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces and mathematical analysis.

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