Some Pexider-type generalizations of the symmetrized multiplicative functional equation on monoids

2019 ◽  
Vol 95 (1-2) ◽  
pp. 249-257
Author(s):  
Bruce Ebanks
Keyword(s):  
Functional Equation ◽  
Multiplicative Functional

scholarly journals On a functional equation that has the quadratic-multiplicative property

2020 ◽  
Vol 18 (1) ◽  
pp. 837-845 ◽  
Author(s):  
Choonkil Park ◽  
Kandhasamy Tamilvanan ◽  
Ganapathy Balasubramanian ◽  
Batool Noori ◽  
Abbas Najati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Multiplicative Property ◽  
Multiplicative Functional

Abstract In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation: \phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v)] by using the direct method and the fixed point method.

The one-level functional equation of multi-rate loss systems

2003 ◽  
Vol 14 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Harro L. Hartmann ◽  
Martin Knoke
Keyword(s):  
Functional Equation ◽  
Loss Systems ◽  
The One ◽  
Rate Loss

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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