scholarly journals Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces

2009 ◽  
Vol 71 (11) ◽  
pp. 5629-5643 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Mixed Type ◽  
Additive Functional ◽  
Additive Functional Equation

scholarly journals Hyers-Ulam stability of a finite variable mixed type quadratic-additive functional equation in quasi-Banach spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5993-6005 ◽  
Author(s):  
K. Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Mixed Type ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation

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 Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation

2011 ◽  
Vol 2011 (1) ◽  
pp. 95
Author(s):  
Madjid Gordji ◽  
Mahdie Kamyar ◽  
Hamid Khodaei ◽  
Dong Shin ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Mixed Type ◽  
Additive Functional ◽  
Additive Functional Equation

scholarly journals Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
K. Tamilvanan ◽  
G. Balasubramanian ◽  
Nazek Alessa ◽  
K. Loganathan
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonnegative Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.

scholarly journals AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
R. Khodabakhsh ◽  
S.-M. Jung ◽  
H. Khodaei
Keyword(s):  
Functional Equation ◽  
Mixed Type ◽  
Additive Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Additive Functional Equation

We prove the generalized Hyers-Ulam stability of generalized mixed type of quartic, cubic, quadratic and additive functional equation in non-Archimedean spaces.

scholarly journals Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1125 ◽  
Author(s):  
Sang Og Kim ◽  
John Michael Michael Rassias
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Integral Equations ◽  
Banach Algebras ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Modular Spaces ◽  
Jordan Triple Product ◽  
Differential And Integral Equations

In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without Δ 2 -conditions. We study the same problem in fuzzy Banach spaces and β -homogeneous Banach spaces. We show the hyperstability of the functional equation associated with the Jordan triple product in fuzzy Banach algebras. The obtained results can be applied to differential and integral equations with kernels of non-power types.

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