scholarly journals Stability of a mixed type additive, quadratic and cubic functional equation in random normed spaces

Filomat ◽  
2011 ◽  
Vol 25 (3) ◽  
pp. 43-54 ◽  
Author(s):  
Eshaghi Gordji ◽  
Bavand Savadkouhi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Mixed Type ◽  
Stability Result ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces ◽  
The Stability

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x+3y)+f(x?3y)= 9(f(x+y)+f(x?y))?16f(x).

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 ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Problems ◽  
Random Normed Spaces ◽  
The Stability

We investigate the stability problems for then-dimensional mixed-type additive and quadratic functional equation2f(∑j=1nxj)+∑1≤i,j≤n,  i≠jf(xi-xj)=(n+1)∑j=1nf(xj)+(n-1)∑j=1nf(-xj)in random normed spaces by applying the fixed point method.

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.

scholarly journals Probabilistic (Quasi)metric Versions for a Stability Result of Baker

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Dorel Miheţ ◽  
Claudia Zaharia
Keyword(s):  
Functional Equation ◽  
Stability Result ◽  
Fixed Point Method ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Triangular Norms ◽  
Random Normed Spaces ◽  
The Stability ◽  
Probabilistic Metric ◽  
Additive Cauchy Functional Equation

By using the fixed point method, we obtain a version of a stability result of Baker in probabilistic metric and quasimetric spaces under triangular norms of Hadžić type. As an application, we prove a theorem regarding the stability of the additive Cauchy functional equation in random 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.

scholarly journals Solution and stability of a mixed type functional equation

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1229-1239 ◽  
Author(s):  
Pasupathi Narasimman ◽  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Mixed Type ◽  
Cubic Functional Equation ◽  
The Stability ◽  
Rassias Stability

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the new mixed type additive and cubic functional equation 3f(x+3y) - f(3x+y)=12[f(x+y)+f(x-y)] - 16[f(x)+f(y)]+12f(2y)-4f(2x). As some corollaries, we show that the stability of this equation can be controlled by the sum and product of powers of norms.

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