The Ulam stability of functional equation on matrix random normed spaces

2018 ◽  
Vol 35 (1) ◽  
pp. 99
Author(s):  
Aimin SONG ◽  
Yuewu LI
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
Stability Of Functional Equation

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 Generalized Hyers-Ulam stability of general cubic functional equation in random normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 89-98
Author(s):  
Seong Kim ◽  
John Rassias ◽  
Nawab Hussain ◽  
Yeol Cho
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces

In this paper, we investigate the generalized Hyers-Ulam stability of a general cubic functional equation: f(x+ky)-kf(x+y)+kf(x-y) -f(x-ky)=2k(k2-1)f(y) for fixed k ? Z+ with k ? 2 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 The cubic ρ-functional equation in matrix non-Archimedean random normed spaces

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2643-2653
Author(s):  
Zhihua Wang ◽  
Chaozhu Hu
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Real Number ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces

Using the direct method and fixed point method, we investigate the Hyers-Ulam stability of the following cubic ?-functional equation f(x+2y) + f(x-2y)- 2f(x+y)-2f(x-y)-12f(x) = ?(4f(x+y/2) + 4f(x-y/2)-f(x+y)-f(x-y)-6f(x)) in matrix non-Archimedean random normed spaces, where ? is a fixed real number with ? ? 2.

scholarly journals Ulam stability of a functional equation deriving from quadratic and additive mappings in random normed spaces

2021 ◽  
Vol 6 (1) ◽  
pp. 908-924 ◽  
Author(s):  
Kandhasamy Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
Additive Mappings

scholarly journals GENERALIZED STABILITY OF AN ADDITIVE-QUADRATIC FUNCTIONAL EQUATION IN VARIOUS SPACES

2019 ◽  
Vol 24 (3) ◽  
Author(s):  
SHAYMAA ALSHYBANI
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Additive Mapping ◽  
Subject Classification ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
Fixed Point Methods

  ABSTRACT. In this paper, using the direct and fixed point methods, we have established the generalized Hyers-Ulam stability of the following additive-quadratic functional equation in non-Archimedean and intuitionistic random normed spaces.   AMS 2010 Subject Classification: 39B82, 39B52, 46S40. Keywords. generalized Hyers-Ulam stability; additive mapping; quadratic mapping; non-Archimedean random normed spaces; intuitionistic random normed spaces; fixed point.

scholarly journals Random Stability of Quadratic Functional Equations

2019 ◽  
Vol 16 (1) ◽  
pp. 498-507
Author(s):  
Mee Kwang Kang
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
Fixed Positive Integer

In this paper, we investigate the generalized Hyers-Ulam stability on random -normed spaces associated with the following generalized quadratic functional equation ,where  is a fixed positive integer via two methods

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-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.

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