Results 31 to 40 of about 103 (93)

Estimation of Inexact Multimixed Additive‐Quadratic Mappings in Fuzzy Normed Spaces

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In the current study, we introduce a new model of multimixed additive‐quadratic mapping and then show that the system of several mixed additive‐quadratic equations defining a multimixed additive‐quadratic mapping can be unified and presented as a single equation. We also show that such mappings under some conditions are multi‐additive, multi‐quadratic,
Abasalt Bodaghi, Pramita Mishra
wiley   +1 more source

On Almost Everywhere K-Additive Set-Valued Maps

Annales Mathematicae Silesianae
Let X be an Abelian group, Y be a commutative monoid, K ⊂Y be a submonoid and F : X → 2Y \ {∅} be a set-valued map. Under some additional assumptions on ideals ℐ1 in X and ℐ2 in X2, we prove that if F is ℐ2-almost everywhere K-additive, then there ...
Jabłońska Eliza
doaj   +1 more source

On a functional equation that has the quadratic-multiplicative property

Open Mathematics, 2020
In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil, Tamilvanan Kandhasamy, Balasubramanian Ganapathy, Noori Batool, Najati Abbas   +4 more
doaj   +1 more source

Fixed Point Technique: Stability Analysis of Quadratic Functional Equation in Various Quasi‐Banach Spaces

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this present work, we derive the solution of a quadratic functional equation and investigate the Ulam stability of this equation in Banach spaces using fixed point and direct techniques. Mainly, we examine the stability results in quasi‐β‐Banach spaces and quasi‐fuzzy β‐Banach spaces by means of direct method as well as quasi‐Banach spaces by means ...
Kandhasamy Tamilvanan, Faruk Özger, S. A. Mohiuddine, Naeem Ahmad, Masho Jima Kabeto, Valerii Obukhovskii   +5 more
wiley   +1 more source

Stability Results for Some Functional Equations on 2‐Banach Spaces With Restricted Domains

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We have a normed abelian group G,.∗,+ and a 2‐pre‐Hilbert space Y with linearly independent elements u and v. Our goal is to prove that any odd map f:G⟶Y satisfying the inequality ‖f(x) + f(y), z‖ ⩽ ‖f(x + y), z‖, z ∈ {u, v}, for all x,y∈G with ‖x‖∗ + ‖y‖∗ ≥ d and some d ≥ 0, is additive. Then, we examined the stability issue correlated with Cauchy and
M. R. Abdollahpour, A. Najati, Y. Khedmati Yengejeh, Ali Jaballah   +3 more
wiley   +1 more source

Thermal Applications of Stability Analysis of Cubic Functional Equation in Banach Spaces and Intuitionistic Fuzzy Normed Spaces

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper analyzes the stability of the Euler–Lagrange–Jensen cubic functional equation in the context of Banach spaces and Intuitionistic Fuzzy Normed Spaces (IFN‐Spaces). We use both direct and fixed point techniques to establish the generalized Ulam stability of the cubic functional equation under various norm‐based constraints.
Subramani Karthikeyan, Kandhasamy Tamilvanan, John Michael Rassias, Masho Jima Kabeto, Nan-Jing Huang   +4 more
wiley   +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  

Generalized Hyers–Ulam stability of mixed-type additive-quartic mappings in 2-Banach spaces

Demonstratio Mathematica
This paper aims to explore the stability of a mixed-type additive-quartic functional equation in 2-Banach spaces via the direct method. We categorize mappings satisfying a certain functional inequality into odd, even, and general mappings, and establish ...
Ponmana Selvan Arumugam, Onitsuka Masakazu, Lakshmi Velu   +2 more
doaj   +1 more source

and Ashish, On the stability of generalized Cauchy linear functional equations, Int

, 2020
We investigate the following generalized Cauchy linear functional equation where a is an arbitrary number and prove the Hyers-Ulam-Rassias stability of the functional equations on Banach spaces.
Renu Chugh, Ashish
core  

Stability of an additive-quadratic functional equation in modular spaces

Open Mathematics
Using the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complete convex modular ...
Baza Abderrahman, Rossafi Mohamed, Park Choonkil, Donganont Mana   +3 more
doaj   +1 more source