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

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

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard

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.


2020 ◽  
Vol 5 (6) ◽  
pp. 5993-6005 ◽  
Author(s):  
K. Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1753-1771
Author(s):  
Azadi Kenary ◽  
M.H. Eghtesadifard

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.


2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
A. Ebadian ◽  
N. Ghobadipour ◽  
Th. M. Rassias ◽  
M. Eshaghi Gordji

We investigate the generalized Hyers-Ulam stability of the functional inequalities∥f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)∥≤∥2f(x)∥and∥f((y−x)/3)+f((x−3z)/3)+f((3x+3z−y)/3)∥≤∥f(x)∥in non-Archimedean normed spaces in the spirit of the Th. M. Rassias stability approach.


2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Janfada ◽  
R. Shourvazi

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following -dimensional functional equation , , on non-Archimedean normed spaces.


2017 ◽  
Vol 35 (1) ◽  
pp. 43 ◽  
Author(s):  
Abasalt Bodaghi

In the current work, we introduce a general form of a mixed additive and quartic functional equation. We determine all solutions of this functional equation. We also establish the generalized Hyers-Ulam stability of this new functional equation in quasi-$\beta$-normed spaces.


2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Soo Hwan Kim

We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation fx⊕y=fx⊕fy in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space.


Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.


2003 ◽  
Vol 2003 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Soon-Mo Jung ◽  
Byungbae Kim

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains.


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