Results 21 to 30 of about 94 (84)

A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms

Annales Mathematicae Silesianae, 2022
Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y),      x,y ∈ S,
Akkaoui Ahmed, El Fatini Mohamed, Fadli Brahim   +2 more
doaj   +1 more source

Hyers–Ulam Stability of Mixed Quintic and Sextic Equations in Matrix‐Valued Non‐Archimedean Random Normed Spaces via Fixed Point Methods

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper establishes the Hyers–Ulam stability of mixed quintic and sextic functional equations within matrix non‐Archimedean random normed spaces. Using fixed‐point techniques, we derive conditions under which approximate solutions guarantee exact solutions, generalizing stability results to these structured probabilistic spaces.
Khalil Shahbazpour, Ali Ebadian, Ali Jabbari, A. M. Nagy   +3 more
wiley   +1 more source

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

Journal of Inequalities and Applications, 2011
In this paper, we prove the generalized Hyers-Ulam stability of generalized mixed type cubic, quadratic, and additive functional equation, in fuzzy Banach spaces. 2010 Mathematics Subject Classification: 39B82; 39B52.
Shin Dong, Park Choonkil, Gordji Madjid, Kamyar Mahdie, Khodaei Hamid   +4 more
doaj  

Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces

Demonstratio Mathematica, 2023
This article presents the general solution f:G→Vf:{\mathcal{G}}\to {\mathcal{V}} of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G,f\left(x)-4f\left(x+y)+6f\left(x+2y)-4f\left(x+3y)+f\left(x+4y)=0,\hspace{1.0em}x,y\in {\
Park Choonkil, Tareeghee Mohammad Amin, Najati Abbas, Yengejeh Yavar Khedmati, Paokanta Siriluk   +4 more
doaj   +1 more source

A Functional equation related to inner product spaces in non-archimedean normed spaces

Advances in Difference Equations, 2011
In this paper, we prove the Hyers-Ulam stability of a functional equation related to inner product spaces in non-Archimedean normed spaces. 2010 Mathematics Subject Classification: Primary 46S10; 39B52; 47S10; 26E30; 12J25.
shin Dong, Park Choonkil, Gordji Madjid, Khodabakhsh Razieh, Khodaei Hamid   +4 more
doaj  

The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

Demonstratio Mathematica, 2020
In 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),f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]
Thanyacharoen Anurak, Sintunavarat Wutiphol   +1 more
doaj   +1 more source

Nonlinear approximation of an ACQ-functional equation in nan-spaces

Fixed Point Theory and Applications, 2011
In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam stability of an additive-cubic-quartic functional equation in NAN-spaces. Mathematics Subject Classification (2010) 39B52·47H10·26E30·46S10·
Lee Jung, Park Choonkil, Azadi Kenary Hassan   +2 more
doaj  

A Functional Equation with Biadditive Functions

Annales Mathematicae Silesianae, 2022
Let S, H, X be groups. For two given biadditive functions A : S2 → X, B : H2 → X and for two unknown mappings T : S → H, g : S → S we will study the functional ...
Łukasik Radosław
doaj   +1 more source

Approximately cubic functional equations and cubic multipliers

Journal of Inequalities and Applications, 2011
In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions.
Alias Idham, Bodaghi Abasalt, Ghahramani Mohammad   +2 more
doaj  

Fuzzy stability of multi-additive mappings

Demonstratio Mathematica
The main aim of this study is to establish some stability results concerning the multi-additive mappings by applying the so-called direct (Hyers) method and the alternative fixed approach in the setting of fuzzy normed spaces.
Park Choonkil, Bodaghi Abasalt, Donganont Mana   +2 more
doaj   +1 more source