Stability of Additive-Quadratic 3D Functional Equation in Modular Spaces by Direct Method

2021 ◽  
Author(s):  
John M. Rassias ◽  
S. Karthikeyan
Keyword(s):  
Functional Equation ◽  
Direct Method ◽  
Modular 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 Stability of an additive-quartic functional equation in modular spaces

2021 ◽  
Vol 26 (01) ◽  
pp. 22-40
Author(s):  
S. Karthikeyan ◽  
C. Park ◽  
P. Palani ◽  
T. R. K. Kumar
Keyword(s):  
Functional Equation ◽  
Modular Spaces ◽  
Quartic Functional Equation

scholarly journals Approximately Ternary Homomorphisms onC*-Ternary Algebras

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Eon Wha Shim ◽  
Su Min Kwon ◽  
Yun Tark Hyen ◽  
Yong Hun Choi ◽  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Direct Method ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Ternary Algebras

Gordji et al. established the Hyers-Ulam stability and the superstability ofC*-ternary homomorphisms andC*-ternary derivations onC*-ternary algebras, associated with the following functional equation:fx2-x1/3+fx1-3x3/3+f3x1+3x3-x2/3=fx1, by the direct method. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the conditions and prove the corrected theorems. Furthermore, we prove the Hyers-Ulam stability and the superstability ofC*-ternary homomorphisms andC*-ternary derivations onC*-ternary algebras by using a fixed point approach.

scholarly journals Stability of an n-variable mixed type functional equation in probabilistic modular spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5903-5915
Author(s):  
Murali Ramdoss ◽  
◽  
Divyakumari Pachaiyappan ◽  
Inho Hwang ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Functional Equation ◽  
Mixed Type ◽  
Modular Spaces

scholarly journals Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy Banach spaces.

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.

Stability of Cauchy-Jensen Mappings in Non-Archimedean Normed Spaces

2013 ◽  
Vol 373-375 ◽  
pp. 1935-1938
Author(s):  
Hai Yan Xue ◽  
Pei Sheng Ji
Keyword(s):  
Functional Equation ◽  
Direct Method ◽  
Normed Spaces

In this paper, we prove stability of the CauchyJensen functional equation in non-Archimedean normed spaces, using the so-called direct method.

On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces

2017 ◽  
Vol 67 (1) ◽  
Author(s):  
Iz-iddine EL-Fassi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Modular Spaces ◽  
Generalized Orthogonal ◽  
Rassias Stability

AbstractIn this paper, we establish the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type

scholarly journals Stability of an additive-quadratic-quartic functional equation

2020 ◽  
Vol 53 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Gwang Hui Kim ◽  
Yang-Hi Lee
Keyword(s):  
Functional Equation ◽  
Direct Method ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this paper, we investigate the stability of an additive-quadratic-quartic functional equation$$\begin{align*}f(x+2y)& +f(x-2y)-2f(x+y)-2f(-x- y)-2f(x-y)-2f(y-x)\nonumber \\ &+4f(-x)+ 2f(x)-f(2y)-f(-2y)+4f(y)+4f(-y)=0 \end{align*}$$by the direct method in the sense of Găvruta.

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