A quartic functional equation originating from the sum of the medians of a triangle in fuzzy normed space

2020 ◽  
Author(s):  
S. Vijayakumar ◽  
S. Karthikeyan ◽  
John M. Rassias ◽  
B. Baskaran
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Fuzzy Normed Space ◽  
Quartic Functional Equation

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.

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 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 Stability of a Quartic Functional Equation in Restricted Domains

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Jaeyoung Chung ◽  
Yu-Min Ju
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Normed Space ◽  
Stability Problem ◽  
Measure Zero ◽  
Stability Theorem ◽  
Real Normed Space ◽  
Quartic Functional Equation ◽  
Restricted Domains

LetXbe a real normed space andYa Banach space andf:X→Y. We prove the Ulam-Hyers stability theorem for the quartic functional equationf(2x+y)+f(2x-y)-4f(x+y)-4f(x-y)-24f(x)+6f(y)=0in restricted domains. As a consequence we consider a measure zero stability problem of the above inequality whenf:R→Y.

scholarly journals STABILITY OF A CUBIC FUNCTIONAL EQUATION IN FUZZY NORMED SPACE

2011 ◽  
Vol 1 (3) ◽  
pp. 411-425
Author(s):  
K. Ravi ◽  
◽  
J. M. Rassias ◽  
P. Narasimman ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Fuzzy Normed Space ◽  
Cubic Functional Equation

scholarly journals Stability of Fibonacci Functional Equation

2018 ◽  
Vol 14 (1) ◽  
pp. 7469-7474
Author(s):  
Sushma Lather ◽  
Sandeep Singh
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Normed Space ◽  
Fuzzy Normed Space ◽  
Rassias Stability

In this paper, we solve the Fibonacci functional equation, f(x)=f(x-1)+f(x-2) and discuss its generalized Hyers-Ulam-Rassias stability in Banach spaces and stability in Fuzzy normed space.

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