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 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 On the non-Archimedean and random approximately general additive mappings: Direct and fixed point methods

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1753-1771
Author(s):  
Azadi Kenary ◽  
M.H. Eghtesadifard
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Additive Mappings

In this paper, we prove the Hyers-Ulam stability of the following generalized additive functional equation ?1? i < j ? m f(xi+xj/2 + m-2?l=1,kl?i,j) = (m-1)2/2 m?i=1 f(xi) where m is a positive integer greater than 3, in various normed spaces.

scholarly journals Hyers-Ulam-Rassias RNS Approximation of Euler-Lagrange-Type Additive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Azadi Kenary ◽  
H. Rezaei ◽  
A. Ebadian ◽  
A. R. Zohdi
Keyword(s):  
Functional Equation ◽  
Normed Spaces ◽  
Banach Modules ◽  
Random Normed Spaces ◽  
Additive Mappings ◽  
Rassias Stability

Recently the generalized Hyers-Ulam (or Hyers-Ulam-Rassias) stability of the following functional equation∑j=1mf(-rjxj+∑1≤i≤m,i≠jrixi)+2∑i=1mrif(xi)=mf(∑i=1mrixi)wherer1,…,rm∈R, proved in Banach modules over a unitalC*-algebra. It was shown that if∑i=1mri≠0,ri,rj≠0for some1≤i<j≤mand a mappingf:X→Ysatisfies the above mentioned functional equation then the mappingf:X→Yis Cauchy additive. In this paper we prove the Hyers-Ulam-Rassias stability of the above mentioned functional equation in random normed spaces (briefly RNS).

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 Approximate Quadratic-Additive Mappings in Fuzzy Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ick-Soon Chang ◽  
Yang-Hi Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Additive Mappings

We examine the generalized Hyers-Ulam stability of the following functional equation:2fx+y+z+w+f-x-y+z+w+f-x+y-z+w+f-x+y+z-w+fx-y-z+w+fx-y+z-w+fx+y-z-w-5fx-3f-x-5fy-3f-y-5fz-3f-z-5fw-3f-w=0,in the fuzzy normed spaces with the fixed point method.

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 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

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